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JOURNALS // Algebra i Analiz

Algebra i Analiz, 1996, Volume 8, Issue 5, Pages 32–162 (Mi aa736)

The hunt for a Bellman function: applications to estimates for singular integral operators and to other classical problems of harmonic analysis
F. L. Nazarov, S. R. Treil'

This publication is cited in the following articles:
  1. Dachun Yang, Wen Yuan, Mingdong Zhang, “Matrix-Weighted Besov–Triebel–Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-differential, Trace, and Calderón–Zygmund Operators”, Proc. Steklov Inst. Math., 331 (2025), 297–333  mathnet  crossref  crossref  isi
  2. A. I. Parfenov, “Inductive methods for Hardy inequality on trees”, Ufa Math. J., 16:2 (2024), 36–65  mathnet  crossref
  3. St. Petersburg Math. J., 35:6 (2024), 1005–1011  mathnet  crossref
  4. Osekowski A., Rapicki M., “Sharp Weighted Inequalities For Harmonic Maximal Operators”, N. Y. J. Math., 28 (2022), 140–153  isi
  5. Fay I.H., “The Bellman Function Technique in Harmonic Analysis, Vol 186”, Bull. Amer. Math. Soc., 59:2 (2022), 293–296  crossref  isi
  6. Nikolidakis E., “The Bellman Function of the Dyadic Maximal Operator in Connection With the Dyadic Carleson Imbedding Theorem”, Forum Math., 34:3 (2022), 781–792  crossref  isi
  7. Isralowitz J., Pott S., Rivera-Rios I.P., “Sharp a(1) Weighted Estimates For Vector-Valued Operators”, J. Geom. Anal., 31:3 (2021), 3085–3116  crossref  isi
  8. Bownik M., Dziedziul K., Kamont A., “Smooth Orthogonal Projections on Riemannian Manifold”, Potential Anal., 54:1 (2021), 41–94  crossref  isi
  9. Nielsen M., Sikic H., “Muckenhoupt Matrix Weights”, J. Geom. Anal., 31:9 (2021), 8850–8865  crossref  isi
  10. Frazier M., Roudenko S., “Littlewood-Paley Theory For Matrix-Weighted Function Spaces”, Math. Ann., 380:1-2 (2021), 487–537  crossref  isi
  11. Kakaroumpas S., Treil S., ““Small Step” Remodeling and Counterexamples For Weighted Estimates With Arbitrarily “Smooth” Weights”, Adv. Math., 376 (2021), 107450  crossref  isi
  12. Osekowski A., Rapicki M., “Sharp Lorentz-Norm Estimates For Dyadic-Like Maximal Operators”, Studia Math., 257:1 (2021), 87–110  crossref  isi
  13. Osekowski A., Rapicki M., “A Weighted Maximal Weak-Type Inequality”, Mathematika, 67:1 (2021), 145–157  crossref  isi
  14. Isralowitz J., “Matrix Weighted Triebel-Lizorkin Bounds: a Simple Stopping Time Proof”, Proc. Amer. Math. Soc., 149:10 (2021), 4145–4158  crossref  isi
  15. V. A. Borovitskii, N. N. Osipov, A. S. Tselishchev, “On the Bellman function method for operators on martingales”, Dokl. Math., 103:3 (2021), 118–121  mathnet  crossref  crossref  zmath  elib
  16. Osekowski A., “The Dual Conjecture of Muckenhoupt and Wheeden”, Rev. Mat. Iberoam., 37:6 (2021), 2285–2308  crossref  isi
  17. Yuan H., Tang G., Li X., Guo D., Luo L., Luo X., “Online Dispatching and Fair Scheduling of Edge Computing Tasks: a Learning-Based Approach”, IEEE Internet Things J., 8:19 (2021), 14985–14998  crossref  isi
  18. Duong X.T., Li J., Yang D., “Variation of Calderon-Zygmund Operators With Matrix Weight”, Commun. Contemp. Math., 23:07 (2021), 2050062  crossref  isi
  19. Banuelos R., Galazka T., Osekowski A., “A Dual Approach to Burkholder'S Lp Estimates”, Bull. London Math. Soc., 53:4 (2021), 1107–1123  crossref  isi
  20. Kucharski M., “Dimension-Free Estimates For Riesz Transforms Related to the Harmonic Oscillator”, Colloq. Math., 165:1 (2021), 139–161  crossref  isi
  21. Cruz-Uribe D., Isralowitz J., Moen K., Pott S., Rivera-Rios I., “Weak Endpoint Bounds For Matrix Weights”, Rev. Mat. Iberoam., 37:4 (2021), 1513–1538  crossref  isi
  22. Kaminski L., Osekowski A., “An Extension of a Hardy'S Inequality and Its Applications”, Math. Inequal. Appl., 24:3 (2021), 679–694  crossref  isi
  23. Stolyarov D., Vasyunin V., Zatitskiy P., “Sharp Multiplicative Inequalities With Bmo i”, J. Math. Anal. Appl., 492:2 (2020), 124479  crossref  isi
  24. Banuelos R., Brzozowski M., Osekowski A., “Burkholder'S Function and a Weighted l-2 Bound For Stochastic Integrals”, Proc. Amer. Math. Soc., 148:11 (2020), 5013–5028  crossref  isi
  25. Carbonaro A., Dragicevic O., “Convexity of Power Functions and Bilinear Embedding For Divergence-Form Operators With Complex Coefficients”, J. Eur. Math. Soc., 22:10 (2020), 3175–3221  crossref  isi
  26. Nikolidakis E.N., “A Sharp Integral Inequality For the Dyadic Maximal Operator and a Related Stability Result”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 45 (2020), 533–546  crossref  isi
  27. Osekowski A., “Weighted Weak-Type Inequalities For Square Functions”, Math. Inequal. Appl., 23:1 (2020), 267–286  crossref  isi
  28. Betancor J.J., Dalmasso E., Farina J.C., Scotto R., “Bellman Functions and Dimension Free l-P-Estimates For the Riesz Transforms in Bessel Settings”, Nonlinear Anal.-Theory Methods Appl., 197 (2020), 111850  crossref  isi
  29. Carbonaro A., Dragicevic O., “Bilinear Embedding For Divergence-Form Operators With Complex Coefficients on Irregular Domains”, Calc. Var. Partial Differ. Equ., 59:3 (2020), 104  crossref  isi
  30. Osekowski A., “On a(P)-a(Q) Weighted Estimates For Maximal Operators”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 45 (2020), 1171–1185  crossref  isi
  31. Barthe F., Ivanisvili P., “Bobkov'S Inequality Via Optimal Control Theory”, Geometric Aspects of Functional Analysis: Israel Seminar (Gafa) 2017-2019, Vol i, Lect. Notes Math., Lecture Notes in Mathematics, 2256, eds. Klartag B., Milman E., Springer International Publishing Ag, 2020, 49–61  crossref  isi
  32. Liu H.-W., Wang K., “A Characterization of Weighted Carleson Measure Spaces”, Taiwan. J. Math., 23:1 (2019), 103–127  crossref  mathscinet  zmath  isi
  33. Delis A.D., Nikolidakis E.N., “Sharp Integral Inequalities For the Dyadic Maximal Operator and Applications”, Math. Z., 291:3-4 (2019), 1197–1209  crossref  mathscinet  zmath  isi  scopus
  34. Pierce L.B., “The Vinogradov Mean Value Theorem [After Wooley, and Bourgain, Demeter and Guth]”, Asterisque, 2019, no. 407, 479+  crossref  isi
  35. Ivanisvili P., Treil S., “Superexponential Estimates and Weighted Lower Bounds For the Square Function”, Trans. Am. Math. Soc., 372:2 (2019), 1139–1157  crossref  isi
  36. Osekowski A., “A Sharp Estimate For Muckenhoupt Class a Infinity and Bmo”, Positivity, 23:3 (2019), 711–725  crossref  isi
  37. V. Vasyunin, A. Osȩkowski, L. Slavin, “The $ \mathrm{BMO}\rightarrow\mathrm{BLO}$ action of the maximal operator on $\alpha$-trees”, St. Petersburg Math. J., 31:5 (2020), 831–863  mathnet  crossref  isi  elib
  38. Melas A.D., “An Eigenfunction Stability Estimate For Approximate Extremals of the Bellman Function For the Dyadic Maximal Operator on l-P”, Proc. Amer. Math. Soc., 147:8 (2019), 3367–3375  crossref  isi
  39. Domelevo K., Petermichl S., Skreb K.A., “Failure of the Matrix Weighted Bilinear Carleson Embedding Theorem”, Linear Alg. Appl., 582 (2019), 452–466  crossref  isi
  40. UrbinaRomero W., Gaussian Harmonic Analysis, Springer Monographs in Mathematics, Springer International Publishing Ag, 2019  crossref  isi
  41. Bennett J., Bez N., “Generating Monotone Quantities For the Heat Equation”, J. Reine Angew. Math., 756 (2019), 37–63  crossref  isi
  42. Nikolski N., Volberg A., “On the Sign Distributions of Hilbert Space Frames”, Anal. Math. Phys., 9:3 (2019), 1115–1132  crossref  isi
  43. Petermichl S., Pott S., Reguera M.C., “A Matrix Weighted Bilinear Carleson Lemma and Maximal Function”, Anal. Math. Phys., 9:3 (2019), 1163–1180  crossref  isi
  44. Carbonaro A., Dragicevic O., “Bounded Holomorphic Functional Calculus For Nonsymmetric Ornstein-Uhlenbeck Operators”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 19:4 (2019), 1497–1533  isi
  45. Isralowitz J., Moen K., “Matrix Weighted Poincare Inequalities and Applications to Degenerate Elliptic Systems”, Indiana Univ. Math. J., 68:5 (2019), 1327–1377  crossref  isi
  46. Nikolidakis E.N., “Extremal Sequences For the Bellman Function of Three Variables of the Dyadic Maximal Operator Related to Kolmogorov'S Inequality”, Trans. Am. Math. Soc., 372:9 (2019), 6315–6342  crossref  isi
  47. Osekowski A., “Weighted Square Function Inequalities”, Publ. Mat., 62:1 (2018), 75–94  crossref  mathscinet  zmath  isi  scopus  scopus
  48. Osekowski A., “Sharp Logarithmic Estimates For Positive Dyadic Shifts”, Adv. Math., 324 (2018), 118–147  crossref  mathscinet  zmath  isi  scopus  scopus
  49. Banuelos R., Osekowski A., “Weighted l-2 Inequalities For Square Functions”, Trans. Am. Math. Soc., 370:4 (2018), 2391–2422  crossref  mathscinet  zmath  isi  scopus  scopus
  50. Banuelos R., Osekowski A., “A Weighted Maximal Inequality For Differentially Subordinate Martingales”, Proc. Amer. Math. Soc., 146:5 (2018), 2263–2275  crossref  mathscinet  zmath  isi  scopus  scopus
  51. Wrobel B., “Dimension-Free l-P Estimates For Vectors of Riesz Transforms Associated With Orthogonal Expansions”, Anal. PDE, 11:3 (2018), 745–773  crossref  mathscinet  zmath  isi  scopus  scopus
  52. Osekowski A., “Sharp l-P-Bounds For the Martingale Maximal Function”, Tohoku Math. J., 70:1 (2018), 121–138  crossref  mathscinet  zmath  isi
  53. Isralowitz J., “A Matrix Weighted T1 Theorem For Matrix Kernelled Czos and a Matrix Weighted John-Nirenberg Theorem”, J. Geom. Anal., 28:2 (2018), 1869–1902  crossref  mathscinet  zmath  isi  scopus
  54. Osekowski A., “Weighted Maximal Inequalities For the Haar System”, Mon.heft. Math., 186:2 (2018), 321–336  crossref  mathscinet  zmath  isi  scopus
  55. Delis A.D., Nikolidakis E.N., “Sharp and General Estimates For the Bellman Function of Three Integral Variables Related to the Dyadic Maximal Operator”, Colloq. Math., 153:1 (2018), 27–37  crossref  mathscinet  zmath  isi  scopus
  56. Ivanisvili P. Stolyarov D.M. Vasyunin I V. Zatitskiy P.B., “Bellman Function For Extremal Problems in Bmo II: Evolution”, Mem. Am. Math. Soc., 255:1220 (2018), 1+  mathscinet  isi
  57. Kovac V., Skreb K.A., “Bellman Functions and l-P Estimates For Paraproducts”, Prob. Math. Stat.., 38:2 (2018), 459–479  crossref  mathscinet  zmath  isi  scopus
  58. Carbonaro A. Dragicevic O., “Functional calculus for generators of symmetric contraction semigroups”, Duke Math. J., 166:5 (2017), 937–974  crossref  mathscinet  zmath  isi  scopus
  59. Osekowski A., “Weighted Inequalities For Martingale Transforms and Stochastic Integrals”, Mathematika, 63:2 (2017), 433–450  crossref  mathscinet  zmath  isi  scopus  scopus
  60. Osekowski A., “Sharp Weighted Bounds For Geometric Maximal Operators”, Glasg. Math. J., 59:3, 3 (2017), 533–547  crossref  mathscinet  zmath  isi  scopus
  61. Osekowski A., “Best Constants in Muckenhoupt'S Inequality”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 42:2 (2017), 889–904  crossref  mathscinet  zmath  isi  scopus  scopus
  62. Osekowski A., “Two-Weight Inequalities For Geometric Maximal Operators”, Math. Inequal. Appl., 20:4 (2017), 1121–1138  crossref  mathscinet  zmath  isi  scopus
  63. Melas A.D., Nikolidakis E.N., “Sharp Lorentz Estimates For Dyadic-Like Maximal Operators and Related Bellman Functions”, J. Geom. Anal., 27:4 (2017), 2644–2657  crossref  mathscinet  zmath  isi  scopus
  64. Pott S., Stoica A., “Bounds For Calderon-Zygmund Operators With Matrix a(2) Weights”, Bull. Sci. Math., 141:6 (2017), 584–614  crossref  mathscinet  zmath  isi  scopus
  65. Nikolidakis E.N., “Extremal Sequences For the Bellman Function of the Dyadic Maximal Operator and Applications to the Hardy Operator”, Can. J. Math.-J. Can. Math., 69:6 (2017), 1364–1384  crossref  mathscinet  zmath  isi  scopus
  66. Bickel K., Lunceford K., Mukhtar N., “Characterizations of a(2) Matrix Power Weights”, J. Math. Anal. Appl., 453:2 (2017), 985–999  crossref  mathscinet  zmath  isi  scopus
  67. Melas A.D., Nikolidakis E.N., “Local Lower Norm Estimates For Dyadic Maximal Operators and Related Bellman Functions”, J. Geom. Anal., 27:3 (2017), 1940–1950  crossref  mathscinet  zmath  isi  scopus
  68. Banuelos R., Osekowski A., “Sharp Weak Type Inequalities For Fractional Integral Operators”, Potential Anal., 47:1 (2017), 103–121  crossref  mathscinet  zmath  isi  scopus
  69. Ivanisvili P., Jaye B., Nazarov F., “Lower Bounds For Uncentered Maximal Functions in Any Dimension”, Int. Math. Res. Notices, 2017, no. 8, 2464–2479  crossref  mathscinet  isi  scopus
  70. Nikolidakis E.N., “the Bellman Function of the Dyadic Maximal Operator Related to Kolmogorov'S Inequality”, Isr. J. Math., 219:2 (2017), 507–528  crossref  mathscinet  zmath  isi  scopus
  71. Hanninen T.S., “Two-Weight Inequality For Operator-Valued Positive Dyadic Operators By Parallel Stopping Cubes”, Isr. J. Math., 219:1 (2017), 71–114  crossref  mathscinet  zmath  isi  scopus
  72. Melas A.D., Nikolidakis E.N., Cheliotis D., “Estimates For Bellman Functions Related to Dyadic-Like Maximal Operators on Weighted Spaces”, Studia Math., 239:1 (2017), 1–16  crossref  mathscinet  zmath  isi  scopus
  73. Isralowitz J., “Boundedness of Commutators and H-Bmo Duality in the Two Matrix Weighted Setting”, Integr. Equ. Oper. Theory, 89:2 (2017), 257–287  crossref  mathscinet  zmath  isi  scopus  scopus
  74. Isralowitz J., Kwon H.-K., Pott S., “Matrix Weighted Norm Inequalities For Commutators and Paraproducts With Matrix Symbols”, J. Lond. Math. Soc.-Second Ser., 96:1 (2017), 243–270  crossref  mathscinet  zmath  isi  scopus  scopus
  75. Loga Ch.R., “An Extension Theorem For Matrix Weighted Sobolev Spaces on Lipschitz Domains”, Houst. J. Math., 43:4 (2017), 1209–1233  mathscinet  zmath  isi
  76. Janakiraman P., Volberg A., “New Bellman Functions and Subordination By Orthogonal Martingales in l-P, 1 < P <= 2”, Harmonic Analysis, Partial Differential Equations and Applications: in Honor of Richard l. Wheeden, Applied and Numerical Harmonic Analysis, eds. Chanillo S., Franchi B., Lu G., Perez C., Sawyer E., Springer International Publishing Ag, 2017, 239–273  crossref  mathscinet  zmath  isi  scopus  scopus
  77. Bickel K., Petermichl S., Wick B.D., “Bounds For the Hilbert Transform With Matrix a(2) Weights”, J. Funct. Anal., 270:5 (2016), 1719–1743  crossref  mathscinet  zmath  isi  scopus  scopus
  78. Bickel K., Wick B.D., “a Study of the Matrix Carleson Embedding Theorem With Applications To Sparse Operators”, J. Math. Anal. Appl., 435:1 (2016), 229–243  crossref  mathscinet  zmath  isi  scopus  scopus
  79. Slavin L., “Best Constants For a Family of Carleson Sequences”, Adv. Math., 289 (2016), 685–724  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  80. Ivanisvili P., Osipov N.N., Stolyarov D.M., Vasyunin V.I., Zatitskiy P.B., “Bellman function for extremal problems in BMO”, Trans. Am. Math. Soc., 368:5 (2016), 3415–3468  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  81. Osekowski A., “Sharp Estimates for Lipschitz Class”, J. Geom. Anal., 26:2 (2016), 1346–1369  crossref  mathscinet  zmath  isi  scopus  scopus
  82. Bickel K., Wick B.D., “Well-Localized Operators on Matrix Weighted l-2 Space”, Houst. J. Math., 42:1 (2016), 249–283  mathscinet  zmath  isi
  83. Osekowski A., “Sharp Logarithmic Inequalities for Hardy Operators”, Z. Anal. ihre. Anwend., 35:1 (2016), 1–20  crossref  mathscinet  zmath  isi  scopus  scopus
  84. Osekowski A., “Sharp weighted logarithmic bound for maximal operators”, Arch. Math., 107:6 (2016), 635–644  crossref  mathscinet  zmath  isi  scopus  scopus
  85. Cruz-Uribe D., Moen K., Rodney S., “Matrix
    $$\mathcal {A}_p$$
    A p Weights, Degenerate Sobolev Spaces, and Mappings of Finite Distortion”, J. Geom. Anal., 26:4 (2016), 2797–2830  crossref  mathscinet  zmath  isi  scopus  scopus
  86. Stolyarov D.M. Zatitskiy P.B., “Theory of locally concave functions and its applications to sharp estimates of integral functionals”, Adv. Math., 291 (2016), 228–273  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  87. Osekowski A., “Sharp Inequalities For the Haar System and Martingale Transforms”, Prob. Math. Stat.., 36:1 (2016), 147–164  mathscinet  zmath  isi
  88. Slavin L., Vasyunin V., “Inequalities for BMO on -Trees”, Int. Math. Res. Notices, 2016, no. 13, 4078–4102  crossref  mathscinet  isi  elib  scopus  scopus
  89. Nikolidakis E.N., Melas A.D., “A Sharp Integral Rearrangement Inequality For the Dyadic Maximal Operator and Applications”, Appl. Comput. Harmon. Anal., 38:2 (2015), 242–261  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  90. Osekowski A., “A New Approach To Hardy-Type Inequalities”, Arch. Math., 104:2 (2015), 165–176  crossref  mathscinet  zmath  isi  scopus  scopus
  91. Osekowski A., “A Splitting Procedure For Bellman Functions and the Action of Dyadic Maximal Operators on $L_p$”, Mathematika, 61:1 (2015), 199–212  crossref  mathscinet  zmath  isi  scopus  scopus
  92. Osekowski A., “Sharp Inequalities For Bmo Functions”, Chin. Ann. Math. Ser. B, 36:2 (2015), 225–236  crossref  mathscinet  isi  scopus  scopus
  93. Mauceri G., Spinelli M., “Riesz Transforms and Spectral Multipliers of the Hodge-Laguerre Operator”, J. Funct. Anal., 269:11 (2015), 3402–3457  crossref  mathscinet  zmath  isi  scopus
  94. Osekowski A., “Sharp Weak-Type Estimates For the Dyadic-Like Maximal Operators”, Taiwan. J. Math., 19:4 (2015), 1031–1050  crossref  mathscinet  zmath  isi  elib  scopus
  95. Osekowski A., “a Prophet Inequality For -Bounded Dependent Random Variables”, Positivity, 19:2 (2015), 289–303  crossref  mathscinet  zmath  isi  scopus
  96. Osekowski A., “Weak-l-Infinity Inequalities For Bmo Functions”, N. Y. J. Math., 21 (2015), 699–713  mathscinet  zmath  isi  elib
  97. Banuelos R., Osekowski A., “Weighted Norm Inequalities For Fractional Maximal Operators: a Bellman Function Approach”, Indiana Univ. Math. J., 64:3 (2015), 957–972  crossref  mathscinet  zmath  isi  scopus
  98. Hytonen T., Perez C., Treil S., Volberg A., “Sharp Weighted Estimates for Dyadic Shifts and the a(2) Conjecture”, J. Reine Angew. Math., 2014:687 (2014), 43–86  crossref  mathscinet  zmath  isi  scopus
  99. Domelevo K., Petermichl S., “Sharp l-P Estimates For Discrete Second Order Riesz Transforms”, Adv. Math., 262 (2014), 932–952  crossref  mathscinet  zmath  isi  scopus
  100. Osekowski A., “Sharp $L^{p,\infty} \to L^q$ Estimates For the Dyadic-Like Maximal Operators”, J. Fourier Anal. Appl., 20:5 (2014), 911–933  crossref  mathscinet  zmath  isi  scopus  scopus
  101. Osekowski A., “Maximal Inequalities For Functions of Bounded Lower Oscillation”, Kyushu J. Math., 68:2 (2014), 297–305  crossref  mathscinet  zmath  isi  scopus  scopus
  102. Vasyunin V., Volberg A., “Sharp Constants in the Classical Weak Form of the John-Nirenberg Inequality”, Proc. London Math. Soc., 108:6 (2014), 1417–1434  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  103. Osekowski A., “Maximal Weak-Type Inequality For Stochastic Integrals”, Electron. Commun. Probab., 19 (2014), 1–13  crossref  mathscinet  isi  scopus  scopus
  104. Osekowski A., “Sharp Weak Type Inequality For Fractional Integral Operators Associated With D-Dimensional Walsh-Fourier Series”, Integr. Equ. Oper. Theory, 78:4 (2014), 589–600  crossref  mathscinet  zmath  isi  scopus  scopus
  105. Rey G., Reznikov A., “Extremizers and Sharp Weak-Type Estimates For Positive Dyadic Shifts”, Adv. Math., 254 (2014), 664–681  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  106. Osekowski A., “Some Sharp Estimates For the Haar System and Other Bases in $L^1(0,1)$”, Math. Scand., 115:1 (2014), 123–142  crossref  mathscinet  zmath  isi
  107. Carbonaro A., Dragicevic O., “Bellman Function and Linear Dimension-Free Estimates in a Theorem of Bakry”, J. Funct. Anal., 265:7 (2013), 1085–1104  crossref  mathscinet  zmath  isi  scopus
  108. Osekowski A., “Sharp Inequalities for Dyadic a(1) Weights”, Arch. Math., 101:2 (2013), 181–190  crossref  mathscinet  zmath  isi  scopus
  109. Borichev A., Janakiraman P., Volberg A., “Subordination by Conformal Martingales in l-P and Zeros of Laguerre Polynomials”, Duke Math. J., 162:5 (2013), 889–924  crossref  mathscinet  zmath  isi  elib  scopus
  110. Osekowski A., “Weighted Maximal Inequalities for Martingales”, Tohoku Math. J., 65:1 (2013), 75–91  crossref  mathscinet  zmath  isi  scopus
  111. Osekowski A., “Sharp Estimates for Functions of Bounded Lower Oscillation”, Bull. Aust. Math. Soc., 87:1 (2013), 68–81  crossref  mathscinet  zmath  isi  scopus
  112. Borichev A., Janakiraman P., Volberg A., “On Burkholder Function for Orthogonal Martingales and Zeros of Legendre Polynomials”, Am. J. Math., 135:1 (2013), 207–236  crossref  mathscinet  zmath  isi  elib  scopus
  113. Nikolidakis E.N., “Optimal Weak Type Estimates for Dyadic-Like Maximal Operators”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 38:1 (2013), 229–244  crossref  mathscinet  zmath  isi  scopus
  114. Banuelos R., Osekowski A., “Burkholder Inequalities for Submartingales, Bessel Processes and Conformal Martingales”, Am. J. Math., 135:6 (2013), 1675–1698  crossref  mathscinet  zmath  isi  scopus
  115. Melas A.D., Nikolidakis E., Stavropoulos T., “Sharp Local Lower l-P-Bounds for Dyadic-Like Maximal Operators”, Proc. Amer. Math. Soc., 141:9 (2013), 3171–3181  crossref  mathscinet  zmath  isi  elib  scopus
  116. Dragicevic O., Volberg A., “Linear dimension-free estimates in the embedding theorem for Schrodinger operators”, J London Math Soc (2), 85:1 (2012), 191–222  crossref  mathscinet  zmath  isi  scopus  scopus
  117. Nielsen M., “On Transference of Multipliers on Matrix Weighted L-p-Spaces”, J Geom Anal, 22:1 (2012), 12–22  crossref  mathscinet  zmath  isi  scopus  scopus
  118. Vasyunin V. Volberg A., “Burkholder's Function via Monge-Ampere Equation”, Ill. J. Math., 54:4, SI (2012), 1393–1428  mathscinet  isi
  119. Janakiraman P., “Orthogonality in Complex Martingale Spaces and Connections with the Beurling-Ahlfors Transform”, Ill. J. Math., 54:4, SI (2012), 1509–1563  mathscinet  isi
  120. Huang P.-K., Wang K., “Some Operators Acting on Weighted Sequence Besov Spaces and Applications”, Taiwan. J. Math., 16:4 (2012), 1507–1530  crossref  mathscinet  zmath  isi  scopus
  121. Kovac V., “Uniform Constants in Hausdorff-Young Inequalities for the Cantor Group Model of the Scattering Transform”, Proc. Amer. Math. Soc., 140:3 (2012), 915–926  crossref  mathscinet  zmath  isi  scopus
  122. Slavin L., Vasyunin V., “Sharp l-P Estimates on Bmo”, Indiana Univ. Math. J., 61:3 (2012), 1051–1110  crossref  mathscinet  zmath  isi  elib  scopus
  123. Kopaliani T., “Higher rank Haar wavelet bases in spaces L-w(p)(R)”, Georgian Math J, 18:3 (2011), 517–532  mathscinet  zmath  isi  elib
  124. Dragicevic O., Volberg A., “Bilinear embedding for real elliptic differential operators in divergence form with potentials”, J Funct Anal, 261:10 (2011), 2816–2828  crossref  mathscinet  zmath  isi  scopus  scopus
  125. Wittwer J., “Survey Article: a User's Guide to Bellman Functions”, Rocky Mountain J Math, 41:3 (2011), 631–661  crossref  mathscinet  zmath  isi  scopus  scopus
  126. Slavin L., Vasyunin V., “Sharp Results in the Integral-Form John-Nirenberg Inequality”, Trans Amer Math Soc, 363:8 (2011), 4135–4169  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  127. Kovac V., “Bellman Function Technique for Multilinear Estimates and an Application to Generalized Paraproducts”, Indiana Univ. Math. J., 60:3 (2011), 813–846  crossref  mathscinet  zmath  isi  elib  scopus
  128. Melas A.D., Nikolidakis E., “Dyadic–Like Maximal Operators on Integrable Functions and Bellman Functions Related to Kolmogorov's Inequality”, Transactions of the American Mathematical Society, 362:3 (2010), 1571–1597  crossref  mathscinet  zmath  isi  scopus  scopus
  129. Nielsen M., “Trigonometric bases for matrix weighted L-p-spaces”, Journal of Mathematical Analysis and Applications, 371:2 (2010), 784–792  crossref  mathscinet  zmath  isi  scopus  scopus
  130. Moen K., “Multiparameter weights with connections to Schauder bases”, Journal of Mathematical Analysis and Applications, 371:1 (2010), 266–281  crossref  mathscinet  zmath  isi  scopus  scopus
  131. Banuelos R., “The Foundational Inequalities of D. l. Burkholder and Some of their Ramifications”, Ill. J. Math., 54:3 (2010), 789–868  mathscinet  zmath  isi
  132. Melas, AD, “Dyadic-like maximal operators on L log L functions”, Journal of Functional Analysis, 257:6 (2009), 1631  crossref  mathscinet  zmath  isi  scopus  scopus
  133. Pereyra, MC, “Haar multipliers meet Bellman functions”, Revista Matematica Iberoamericana, 25:3 (2009), 799  crossref  mathscinet  zmath  isi  scopus  scopus
  134. Dragicevic, O, “Bellman function and bilinear embedding theorem for Schrodinger-type operators”, Comptes Rendus Mathematique, 347:9–10 (2009), 537  crossref  mathscinet  zmath  isi  scopus  scopus
  135. Bilyk, D, “Composition of Haar paraproducts: the random case”, Analysis Mathematica, 35:1 (2009), 1  crossref  mathscinet  zmath  isi  scopus  scopus
  136. Melas, AD, “Sharp general local estimates for dyadic-like maximal operators and related Bellman functions”, Advances in Mathematics, 220:2 (2009), 367  crossref  mathscinet  zmath  isi  scopus  scopus
  137. V. I. Vasyunin, “Mutual estimates of $L^p$-norms, and the Bellman function”, J. Math. Sci. (N. Y.), 156:5 (2009), 766–798  mathnet  crossref  zmath
  138. Melas, AD, “On weak type inequalities for dyadic maximal functions”, Journal of Mathematical Analysis and Applications, 348:1 (2008), 404  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  139. Haroske, DD, “Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis”, Mathematische Nachrichten, 281:10 (2008), 1476  crossref  mathscinet  zmath  isi  scopus  scopus
  140. Petermichl, S, “Heating of the Beurling operator: Sufficient conditions for the two-weight case”, Studia Mathematica, 186:3 (2008), 203  crossref  mathscinet  zmath  isi  scopus  scopus
  141. Nazarov, F, “Two weight inequalities for individual Haar multipliers and other well localized operators”, Mathematical Research Letters, 15:2–3 (2008), 583  crossref  mathscinet  zmath  isi
  142. Slavin, L, “Monge-Ampere equations and Bellman functions: The dyadic maximal operator”, Comptes Rendus Mathematique, 346:9–10 (2008), 585  crossref  mathscinet  zmath  isi  elib  scopus  scopus
  143. Frazier M., Roudenko S., “Traces and extensions of matrix–weighted Besov spaces”, Bulletin of the London Mathematical Society, 40:2 (2008), 181–192  crossref  mathscinet  zmath  isi  scopus
  144. Petermichl, S, “The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical A(p) characteristic”, American Journal of Mathematics, 129:5 (2007), 1355  crossref  mathscinet  zmath  isi  scopus  scopus
  145. Pott S., “A sufficient condition for the boundedness of operator–weighted martingale transforms and Hilbert transform”, Studia Mathematica, 182:2 (2007), 99–111  crossref  mathscinet  zmath  isi  scopus  scopus
  146. Lauzon M., “Maximal functions and Calderon–Zygmund theory for vector–valued functions with operator weights”, Indiana University Mathematics Journal, 56:4 (2007), 1723–1748  crossref  mathscinet  isi  scopus  scopus
  147. Lauzon M., Treil S., “Scalar and vector Muckenhoupt weights”, Indiana University Mathematics Journal, 56:4 (2007), 1989–2015  crossref  mathscinet  isi  scopus  scopus
  148. Wittwer J., “Bellman functions and MRA wavelets”, Rocky Mountain Journal of Mathematics, 37:1 (2007), 343–358  crossref  mathscinet  zmath  isi  scopus  scopus
  149. Lacey M.T., “Lectures on Nehari's Theorem on the polydisk”, Topics in Harmonic Analysis and Ergodic Theory, Contemporary Mathematics Series, 444, 2007, 185–213  crossref  mathscinet  zmath  adsnasa  isi
  150. Slavin L., Volberg A., “The s-function and the exponential integral”, Topics in Harmonic Analysis and Ergodic Theory, Contemporary Mathematics Series, 444, 2007, 215–228  crossref  mathscinet  zmath  isi
  151. Slavin L., Volberg A., “Bellman function and the H-1-BMO duality”, Harmonic Analysis, Partial Differential Equations, and Related Topics, Contemporary Mathematics Series, 428, 2007, 113–126  crossref  mathscinet  zmath  isi
  152. Dragicevic, O, “Bellman functions and dimensionless estimates of Littlewood-Paley type”, Journal of Operator Theory, 56:1 (2006), 167  mathscinet  zmath  isi
  153. Dragicevic, O, “Bellman function for the estimates of Littlewood-Paley type and asymptotic estimates in the p-1 problem”, Comptes Rendus Mathematique, 340:10 (2005), 731  crossref  mathscinet  zmath  isi  scopus  scopus
  154. Bownik M., “Atomic and molecular decompositions of anisotropic Besov spaces”, Mathematische Zeitschrift, 250:3 (2005), 539–571  crossref  mathscinet  zmath  isi  scopus  scopus
  155. Dragicevic O., Grafakos L., Pereyra C., Petermichl S., “Extrapolation and sharp norm estimates for classical operators on weighted lebesgue spaces”, Publicacions Matematiques, 49:1 (2005), 73–91  crossref  mathscinet  zmath  isi  scopus  scopus
  156. Melas A.D., “The Bellman functions of dyadic–like maximal operators and related inequalities”, Advances in Mathematics, 192:2 (2005), 310–340  crossref  mathscinet  zmath  isi  scopus  scopus
  157. Frazier M., Roudenko S., “Matrix–weighted Besov spaces and conditions of A(p) type for 0 < p <= 1”, Indiana University Mathematics Journal, 53:5 (2004), 1225–1254  crossref  mathscinet  zmath  isi  scopus  scopus
  158. Roudenko S., “Duality of matrix–weighted Besov spaces”, Studia Mathematica, 160:2 (2004), 129–156  crossref  mathscinet  zmath  isi  scopus  scopus
  159. V. I. Vasyunin, “The sharp constant in the reverse Hölder inequality for the muckenhoupt weights”, St. Petersburg Math. J., 15:1 (2004), 49–79  mathnet  crossref  mathscinet  zmath
  160. Nazarov, F, “The Tb-theorem on non-homogeneous spaces”, Acta Mathematica, 190:2 (2003), 151  crossref  mathscinet  zmath  isi  scopus  scopus
  161. Roudenko, S, “Matrix-weighted Besov spaces”, Transactions of the American Mathematical Society, 355:1 (2003), 273  crossref  mathscinet  zmath  isi  scopus  scopus
  162. Goldberg M., “Matrix A(p) weights via maximal functions”, Pacific Journal of Mathematics, 211:2 (2003), 201–220  crossref  mathscinet  zmath  isi  scopus  scopus
  163. Bownik M., “Anisotropic Hardy spaces and wavelets”, Memoirs of the American Mathematical Society, 164:781 (2003), 1  crossref  mathscinet  isi
  164. Muscalu C., Tao T., Thiele C., “A Carleson type theorem for a Cantor group model of the scattering transform”, Nonlinearity, 16:1 (2003), 219–246  crossref  mathscinet  zmath  adsnasa  isi  scopus
  165. Gohberg I., Kaashoek M.A., Spitkovsky I.M., “An overview of matrix factorization theory and operator applications”, Factorization and Integrable Systems, Operator Theory : Advances and Applications, 141, 2003, 1–102  mathscinet  zmath  isi
  166. Nazarov, F, “The Bellman function, the two-weight Hilbert transform, and embeddings of the model spaces K-0”, Journal D Analyse Mathematique, 87 (2002), 385  crossref  mathscinet  zmath  isi  scopus
  167. Nazarov, F, “Accretive system Tb-theorems on nonhomogeneous spaces”, Duke Mathematical Journal, 113:2 (2002), 259  crossref  mathscinet  zmath  isi  scopus  scopus
  168. Nazarov, F, “Sharp estimates in vector Carleson imbedding theorem and for vector paraproducts”, Journal fur Die Reine und Angewandte Mathematik, 542 (2002), 147  crossref  mathscinet  zmath  isi
  169. Stroethoff K., Zheng D.C., “Invertible Toeplitz products”, Journal of Functional Analysis, 195:1 (2002), 48–70  crossref  mathscinet  zmath  isi  scopus  scopus
  170. Tachizawa, K, “On weighted dyadic Carleson's inequalities”, Journal of Inequalities and Applications, 6:4 (2001), 415  crossref  mathscinet  zmath  isi
  171. Christ, M, “Vector A(2) weights and a Hardy-Littlewood maximal function”, Transactions of the American Mathematical Society, 353:5 (2001), 1995  crossref  mathscinet  zmath  isi
  172. Bownik M., “Inverse volume inequalities for matrix weights”, Indiana University Mathematics Journal, 50:1 (2001), 383–410  crossref  mathscinet  zmath  isi  scopus  scopus
  173. Nazarov F., Treil S., Volberg A., “Bellman function in stochastic control and harmonic analysis”, Systems, Approximation, Singular Integral Operators, and Related Topics, Operator Theory : Advances and Applications, 129, 2001, 393–423  crossref  mathscinet  zmath  isi
  174. Petermichl S., “Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol”, Comptes Rendus de l Academie Des Sciences Serie i–Mathematique, 330:6 (2000), 455–460  crossref  mathscinet  zmath  adsnasa  isi  scopus
  175. Nazarov, F, “The bellman functions and two-weight inequalities for Haar multipliers”, Journal of the American Mathematical Society, 12:4 (1999), 909  crossref  mathscinet  zmath  isi
  176. Treil S., Volberg A., “Continuous frame decomposition and a vector Hunt–Muckenhoupt–Wheeden theorem”, Arkiv For Matematik, 35:2 (1997), 363–386  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  177. Nazarov F., Treil S., Volberg A., “Cauchy integral and Calderon–Zygmund operators on nonhomogeneous spaces”, International Mathematics Research Notices, 1997, no. 15, 703–726  crossref  mathscinet  zmath  isi
  178. Nazarov F., Treil S., Volberg A., “Counterexample to the infinite dimensional Carleson embedding theorem”, Comptes Rendus de l Academie Des Sciences Serie i–Mathematique, 325:4 (1997), 383–388  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus


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