Тепловое расширение оператора Бёрлинга и оценки его нормы
А. Л. Вольберг, Ф. Л. Назаров

Эта публикация цитируется в следующих статьяx:

1. Rodrigo Bañuelos, Daesung Kim, Mateusz Kwaśnicki, “Sharp ℓ inequalities for discrete singular integrals on the lattice Zd”, Journal of Functional Analysis, 2026, 111359  
2. Gaven Martin, Cong Yao, “The $L^p$ Teichmüller Theory: Existence and Regularity of Critical Points”, Arch Rational Mech Anal, 248:2 (2024)  
3. Adam Osȩkowski, “Mixed Lp$L^p$ estimates for transforms of noncommutative martingales”, Bulletin of London Math Soc, 2024  
4. Baudoin F., Chen L., “A Note on Second Order Riesz Transforms in 3-Dimensional Lie Groups”, Arch. Math., 118:3 (2022), 291–304      
5. Banuelos R., Baudoin F., Chen L., Sire Ya., “Multiplier Theorems Via Martingale Transforms”, J. Funct. Anal., 281:9 (2021), 109188      
6. Duse E., “Second Order Elliptic Equations and Hodge-Dirac Operators”, J. Funct. Anal., 281:12 (2021), 109267      
7. Rodrigo Bañuelos, Tomasz Gałązka, Adam Osȩkowski, “A dual approach to Burkholder's Lp estimates”, Bulletin of London Math Soc, 53:4 (2021), 1107  
8. 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        
9. 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        
10. 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        
11. 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    
12. Banuelos R., Osekowski A., “Stability in Burkholder'S Differentially Subordinate Martingales Inequalities and Applications to Fourier Multipliers”, J. Math. Pures Appl., 119 (2018), 1–44          
13. Kovac V. Skreb K.A., “Bellman Functions and l-P Estimates For Paraproducts”, Prob. Math. Stat.., 38:2 (2018), 459–479          
14. Carbonaro A., Dragicevic O., “Functional calculus for generators of symmetric contraction semigroups”, Duke Math. J., 166:5 (2017), 937–974          
15. Strzelecki M., “The L^p-norms of the Beurling–Ahlfors transform on radial functions”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 42:1 (2017), 73–93          
16. Perlmutter M., “a Method of Rotations For Levy Multipliers”, Math. Z., 287:3-4 (2017), 797–816          
17. Nolder C.A., Wang G., “Fourier Multipliers and Dirac Operators”, Adv. Appl. Clifford Algebr., 27:2 (2017), 1647–1657          
18. Osekowski A., “Sharp Logarithmic Inequalities for Hardy Operators”, Z. Anal. ihre. Anwend., 35:1 (2016), 1–20          
19. Arcozzi N., Domelevo K., Petermichl S., “Second Order Riesz Transforms on Multiply–Connected Lie Groups and Processes with Jumps”, Potential Anal., 45:4 (2016), 777–794          
20. Kim D., “Martingale Transforms and the Hardy-Littlewood-Sobolev Inequality for Semigroups”, Potential Anal., 45:4 (2016), 795–807          
21. Perlmutter M., “On a Class of Caldern-Zygmund Operators Arising From Projections of Martingale Transforms”, Potential Anal., 42:2 (2015), 383–401          
22. Banuelos R., Osekowski A., “on Astala'S Theorem For Martingales and Fourier Multipliers”, Adv. Math., 283 (2015), 275–302          
23. Banuelos R., Osekowski A., “Sharp Martingale Inequalities and Applications To Riesz Transforms on Manifolds, Lie Groups and Gauss Space”, J. Funct. Anal., 269:6 (2015), 1652–1713          
24. Astala K., Iwaniec T., Prause I., Saksman E., “a Hunt For Sharp l-P-Estimates and Rank-One Convex Variational Integrals”, Filomat, 29:2 (2015), 245–261          
25. Chen X., Qian T., “Non-Stretch Mappings for a Sharp Estimate of the Beurling-Ahlfors Operator”, J. Math. Anal. Appl., 412:2 (2014), 805–815          
26. Domelevo K. Petermichl S., “Sharp l-P Estimates For Discrete Second Order Riesz Transforms”, Adv. Math., 262 (2014), 932–952          
27. Osekowski A., “On Restricted Weak-Type Constants of Fourier Multipliers”, Publ. Mat., 58:2 (2014), 415–443        
28. Banuelos R., Osekowski A., “On the Bellman Function of Nazarov, Treil and Volberg”, Math. Z., 278:1-2 (2014), 385–399          
29. Domelevo K., Petermichl S., “Sharp l-P Estimates For Discrete Second-Order Riesz Transforms”, C. R. Math., 352:6 (2014), 503–506          
30. Osekowski A., “Maximal Weak-Type Inequality For Stochastic Integrals”, Electron. Commun. Probab., 19 (2014), 1–13        
31. Osekowski A., “Maximal Inequalities For Martingales and Their Differential Subordinates”, J. Theor. Probab., 27:1 (2014), 1–21          
32. Osekowski A., “Logarithmic Inequalities for Fourier Multipliers”, Math. Z., 274:1-2 (2013), 515–530          
33. Banuelos R., Baudoin F., “Martingale Transforms and their Projection Operators on Manifolds”, Potential Anal., 38:4 (2013), 1071–1089          
34. 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            
35. 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            
36. Banuelos R. Osekowski A., “Burkholder Inequalities for Submartingales, Bessel Processes and Conformal Martingales”, Am. J. Math., 135:6 (2013), 1675–1698          
37. Osekowski A., “Sharp Inequalities for the Haar System and Fourier Multipliers”, J. Funct. Space Appl., 2013, 646012          
38. Adam Osȩkowski, “Survey Article: Bellman function method and sharp inequalities for martingales”, Rocky Mountain J. Math., 43:6 (2013)  
39. Astala K., Iwaniec T., Prause I., Saksman E., “Burkholder Integrals, Morrey's Problem and Quasiconformal Mappings”, J Amer Math Soc, 25:2 (2012), 507–531          
40. Banuelos R., Osekowski A., “Martingales and Sharp Bounds for Fourier Multipliers”, Ann Acad Sci Fenn Math, 37:1 (2012), 251–263          
41. Vasyunin V., Volberg A., “Burkholder's Function via Monge-Ampere Equation”, Ill. J. Math., 54:4, SI (2012), 1393–1428    
42. Bogdan K., Wojciechowski L., “Parabolic Martingales and Non-Symmetric Fourier Multipliers”, Prob. Math. Stat.., 32:2 (2012), 241–253      
43. Boros N., Janakiraman P., Volberg A., “Sharp l-P-Bounds for a Small Perturbation of Burkholder's Martingale Transform”, Indiana Univ. Math. J., 61:2 (2012), 751–773          
44. Pattakos N., Volberg A., “A new weighted Bellman function”, C R Math Acad Sci Paris, 349:21–22 (2011), 1151–1154          
45. Dragicevic O., “Some remarks on the L-p estimates for powers of the Ahlfors-Beurling operator”, Arch Math (Basel), 96:5 (2011), 463–471          
46. Petermichl S., Slavin L., Wick B.D., “New Estimates for the Beurling-Ahlfors Operator on Differential Forms”, Journal of Operator Theory, 65:2 (2011), 307–324      
47. Hytonen T.P., “On the Norm of the Beurling-Ahlfors Operator in Several Dimensions”, Canad Math Bull, 54:1 (2011), 113–125          
48. Burgess Davis, Renming Song, Selected Works of Donald L. Burkholder, 2011, 1  
49. Geiss S., Montgomery-Smith S., Saksman E., “On singular integral and martingale transforms”, Trans. Amer. Math. Soc., 362:2 (2010), 553–575          
50. Banuelos R., “The Foundational Inequalities of D. l. Burkholder and Some of their Ramifications”, Ill. J. Math., 54:3 (2010), 789–868      
51. O. Dragicevic, S. Treil, A. Volberg, “A Theorem about Three Quadratic Forms”, International Mathematics Research Notices, 2010  
52. Rodrigo Bañuelos, “The foundational inequalities of D. L. Burkholder and some of their ramifications”, Illinois J. Math., 54:3 (2010)  
53. Vasily Vasyunin, Alexander Volberg, “Burkholder's function via Monge–Ampère equation”, Illinois J. Math., 54:4 (2010)  
54. Prabhu Janakiraman, “Orthogonality in complex martingale spaces and connections with the Beurling–Ahlfors transform”, Illinois J. Math., 54:4 (2010)  
55. Pereyra M.C., “Haar multipliers meet Bellman functions”, Rev. Mat. Iberoamericana, 25:3 (2009), 799–840          
56. Bañuelos R., Janakiraman P., “On the weak-type constant of the Beurling-Ahlfors transform”, Michigan Math. J., 58:2 (2009), 459–477        
57. Dragičević O., Treil S., Volberg A., “A theorem about three quadratic forms”, Int. Math. Res. Not. IMRN, 2008, rnn072, 9 pp.      
58. Petermichl S., Wittwer J., “Heating of the Beurling operator: Sufficient conditions for the two-weight case”, Studia Math., 186:3 (2008), 203–217          
59. Iwaniec T., Martin G., The Beltrami equation, Mem. Amer. Math. Soc., 191, no. 893, 2008, x+92 pp.    
60. Bañuelos R., Janakiraman P., “$L^p$-bounds for the Beurling-Ahlfors transform”, Trans. Amer. Math. Soc., 360:7 (2008), 3603–3612          
61. Petermichl S., “The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical $A_p$ characteristic”, Amer. J. Math., 129:5 (2007), 1355–1375          
62. Bañuelos R., Bogdan K., “Lévy processes and Fourier multipliers”, J. Funct. Anal., 250:1 (2007), 197–213          
63. Dragičević O., Petermichl S., Volberg A., “A rotation method which gives linear $L^p$ estimates for powers of the Ahlfors-Beurling operator”, J. Math. Pures Appl. (9), 86:6 (2006), 492–509          
64. Dragičević O., Volberg A., “Bellman functions and dimensionless estimates of Littlewood-Paley type”, J. Operator Theory, 56:1 (2006), 167–198      
65. Dragičević O., Volberg A., “Bellman function, Littlewood-Paley estimates and asymptotics for the Ahlfors-Beurling operator in $L^p(\mathbb C)$”, Indiana Univ. Math. J., 54:4 (2005), 971–995          
66. Dragičević O., Volberg A., “Bellman function for the estimates of Littlewood-Paley type and asymptotic estimates in the $p-1$ problem”, C. R. Math. Acad. Sci. Paris, 340:10 (2005), 731–734          
67. Kari Astala, Tadeusz Iwaniec, Eero Saksman, “Beltrami operators in the plane”, Duke Math. J., 107:1 (2001)