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

Эта публикация цитируется в следующих статьяx:

1. Gaven Martin, Cong Yao, “The $L^p$ Teichmüller Theory: Existence and Regularity of Critical Points”, Arch Rational Mech Anal, 248:2 (2024)  
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9. 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        
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22. 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          
23. 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          
24. 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          
25. Domelevo K. Petermichl S., “Sharp l-P Estimates For Discrete Second Order Riesz Transforms”, Adv. Math., 262 (2014), 932–952          
26. Osekowski A., “On Restricted Weak-Type Constants of Fourier Multipliers”, Publ. Mat., 58:2 (2014), 415–443        
27. Banuelos R., Osekowski A., “On the Bellman Function of Nazarov, Treil and Volberg”, Math. Z., 278:1-2 (2014), 385–399          
28. Domelevo K., Petermichl S., “Sharp l-P Estimates For Discrete Second-Order Riesz Transforms”, C. R. Math., 352:6 (2014), 503–506          
29. Osekowski A., “Maximal Weak-Type Inequality For Stochastic Integrals”, Electron. Commun. Probab., 19 (2014), 1–13        
30. Osekowski A., “Maximal Inequalities For Martingales and Their Differential Subordinates”, J. Theor. Probab., 27:1 (2014), 1–21          
31. Osekowski A., “Logarithmic Inequalities for Fourier Multipliers”, Math. Z., 274:1-2 (2013), 515–530          
32. Banuelos R., Baudoin F., “Martingale Transforms and their Projection Operators on Manifolds”, Potential Anal., 38:4 (2013), 1071–1089          
33. 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            
34. 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            
35. Banuelos R. Osekowski A., “Burkholder Inequalities for Submartingales, Bessel Processes and Conformal Martingales”, Am. J. Math., 135:6 (2013), 1675–1698          
36. Osekowski A., “Sharp Inequalities for the Haar System and Fourier Multipliers”, J. Funct. Space Appl., 2013, 646012          
37. Adam Osȩkowski, “Survey Article: Bellman function method and sharp inequalities for martingales”, Rocky Mountain J. Math., 43:6 (2013)  
38. 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          
39. Banuelos R., Osekowski A., “Martingales and Sharp Bounds for Fourier Multipliers”, Ann Acad Sci Fenn Math, 37:1 (2012), 251–263          
40. Vasyunin V., Volberg A., “Burkholder's Function via Monge-Ampere Equation”, Ill. J. Math., 54:4, SI (2012), 1393–1428    
41. Bogdan K., Wojciechowski L., “Parabolic Martingales and Non-Symmetric Fourier Multipliers”, Prob. Math. Stat.., 32:2 (2012), 241–253      
42. 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          
43. Pattakos N., Volberg A., “A new weighted Bellman function”, C R Math Acad Sci Paris, 349:21–22 (2011), 1151–1154          
44. Dragicevic O., “Some remarks on the L-p estimates for powers of the Ahlfors-Beurling operator”, Arch Math (Basel), 96:5 (2011), 463–471          
45. 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      
46. Hytonen T.P., “On the Norm of the Beurling-Ahlfors Operator in Several Dimensions”, Canad Math Bull, 54:1 (2011), 113–125          
47. Burgess Davis, Renming Song, Selected Works of Donald L. Burkholder, 2011, 1  
48. Geiss S., Montgomery-Smith S., Saksman E., “On singular integral and martingale transforms”, Trans. Amer. Math. Soc., 362:2 (2010), 553–575          
49. Banuelos R., “The Foundational Inequalities of D. l. Burkholder and Some of their Ramifications”, Ill. J. Math., 54:3 (2010), 789–868      
50. O. Dragicevic, S. Treil, A. Volberg, “A Theorem about Three Quadratic Forms”, International Mathematics Research Notices, 2010  
51. Rodrigo Bañuelos, “The foundational inequalities of D. L. Burkholder and some of their ramifications”, Illinois J. Math., 54:3 (2010)  
52. Vasily Vasyunin, Alexander Volberg, “Burkholder's function via Monge–Ampère equation”, Illinois J. Math., 54:4 (2010)  
53. Prabhu Janakiraman, “Orthogonality in complex martingale spaces and connections with the Beurling–Ahlfors transform”, Illinois J. Math., 54:4 (2010)  
54. Pereyra M.C., “Haar multipliers meet Bellman functions”, Rev. Mat. Iberoamericana, 25:3 (2009), 799–840          
55. Bañuelos R., Janakiraman P., “On the weak-type constant of the Beurling-Ahlfors transform”, Michigan Math. J., 58:2 (2009), 459–477        
56. Dragičević O., Treil S., Volberg A., “A theorem about three quadratic forms”, Int. Math. Res. Not. IMRN, 2008, rnn072, 9 pp.      
57. Petermichl S., Wittwer J., “Heating of the Beurling operator: Sufficient conditions for the two-weight case”, Studia Math., 186:3 (2008), 203–217          
58. Iwaniec T., Martin G., The Beltrami equation, Mem. Amer. Math. Soc., 191, no. 893, 2008, x+92 pp.    
59. Bañuelos R., Janakiraman P., “$L^p$-bounds for the Beurling-Ahlfors transform”, Trans. Amer. Math. Soc., 360:7 (2008), 3603–3612          
60. 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          
61. Bañuelos R., Bogdan K., “Lévy processes and Fourier multipliers”, J. Funct. Anal., 250:1 (2007), 197–213          
62. 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          
63. Dragičević O., Volberg A., “Bellman functions and dimensionless estimates of Littlewood-Paley type”, J. Operator Theory, 56:1 (2006), 167–198      
64. 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          
65. 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          
66. Kari Astala, Tadeusz Iwaniec, Eero Saksman, “Beltrami operators in the plane”, Duke Math. J., 107:1 (2001)