SOME QUESTIONS REGARDING VERIFICATION OF CARLESON MEASURES

doi:10.1007/s10473-021-0620-4

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (6): 2136-2148.doi: 10.1007/s10473-021-0620-4

SOME QUESTIONS REGARDING VERIFICATION OF CARLESON MEASURES

邓方文¹, 欧阳才衡¹, 彭茹²

1. Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China;
2. Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China

收稿日期:2021-05-13 修回日期:2021-09-07 出版日期:2021-12-25 发布日期:2021-12-27
通讯作者: Caiheng OUYANG,E-mail:ouyang@wipm.ac.cn E-mail:ouyang@wipm.ac.cn
作者简介:Fangwen DENG,E-mail:fwdeng@wipm.ac.cn;Guantie DENG,E-mail:pengru79@163.com
基金资助:
Supported by the National Natural Science Foundation of China (11771441, 11601400).

SOME QUESTIONS REGARDING VERIFICATION OF CARLESON MEASURES

Fangwen DENG¹, Caiheng OUYANG¹, Guantie DENG²

1. Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China;
2. Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China

Received:2021-05-13 Revised:2021-09-07 Online:2021-12-25 Published:2021-12-27
Supported by:
Supported by the National Natural Science Foundation of China (11771441, 11601400).

摘要/Abstract

摘要： In this paper, we give a survey of some recent progress in terms of verifying Carleson measures; this includes the difference between two definitions of a Carleson measure, the Bergman tree condition, the T1 condition for Besov-Sobolev spaces on a complex ball, vector-valued Carleson measures, Carleson measures in strongly pseudoconvex domains and reverse Carleson measures.

关键词: Carleson measures, Besov-Sobolev spaces, Hardy spaces, Bergman spaces

Abstract: In this paper, we give a survey of some recent progress in terms of verifying Carleson measures; this includes the difference between two definitions of a Carleson measure, the Bergman tree condition, the T1 condition for Besov-Sobolev spaces on a complex ball, vector-valued Carleson measures, Carleson measures in strongly pseudoconvex domains and reverse Carleson measures.

Key words: Carleson measures, Besov-Sobolev spaces, Hardy spaces, Bergman spaces

中图分类号:

32A37

邓方文, 欧阳才衡, 彭茹. SOME QUESTIONS REGARDING VERIFICATION OF CARLESON MEASURES[J]. 数学物理学报(英文版), 2021, 41(6): 2136-2148.

Fangwen DENG, Caiheng OUYANG, Guantie DENG. SOME QUESTIONS REGARDING VERIFICATION OF CARLESON MEASURES[J]. Acta mathematica scientia,Series B, 2021, 41(6): 2136-2148.

参考文献 22

[1]	Abate M, Mongodi S, Raissy J. Toeplitz operators and skew Carleson measures for weighted Bergman spaces on strongly pseudoconvex domains. J Operator Theory, 2020, 84(2):339-364
[2]	Abate M, Raissy J, Saracco A. Toeplitz operators and Carleson measures in strongly pseudoconvex domains. J Funct Anal, 2012, 263(11):3449-3491
[3]	Abate M, Saracco A. Carleson measures and uniformly discrete sequences in strongly pseudocomvex domains. J London Math Soc, 2011, 83(2):587-605
[4]	Arcozzi N, Rochberg R, Sawyer E. Carleson measures for analytic Besov spaces. Rev Mat Iberoamericana, 2002, 18:443-510
[5]	Arcozzi N, Rochberg R, Sawyer E. Carleson measures and interpolating sequences. Mem Amer Math Soc, 2006, 182(859)
[6]	Arcozzi N, Rochberg R, Sawyer E. Carleson measures for the Drury-Arveson Hardy space and other BesovSobolev spaces on complex balls. Adv Math, 2008, 218:1107-1180
[7]	Carleson L. An interpolation problem for bounded analytic functions. Amer J Math, 1958, 80:921-930
[8]	Carleson L. Interpolations by bounded analytic functions and the corona problem. Ann of Math, 1962, 76:547-559
[9]	Cima J A, Wogen W R. A Carleson measure theorem for the Bergman space on the ball. J Operator Theory, 1982, 7(1):157-165
[10]	Duren P L, Weir R. The pseudohyperbolic metric and Bergman spaces in the ball. Trans Amer Math Soc, 2007, 359:63-76
[11]	Hartmann A, Massaneda X, Nicolau A, Ortega-Cerda J. Reverse Carleson measures in Hardy spaces. Collectanea Math, 2014, 65:357-365
[12]	Hastings W W. A Carleson measure theorem for Bergman spaces. Proc Amer Math Soc, 1975, 52:237-241
[13]	Lefèvre P, Li D, Queffelec H, Rodriguez-Piazza L. Nevanlinna counting function and Carleson function of analytic maps. Math Ann, 2011, 351:305-326
[14]	Lefèvre P, Li D, Queffelec H, Rodriguez-Piazza L. Some revisited results about composition operators on Hardy spaces. Rev Mat Iberoamericana, 2012, 28:57-76
[15]	Luecking D. A technique for characterizing Carleson measure on Bergman spaces. Proc Amer Math Soc, 1983, 87:656-660
[16]	Nazarov F, Treil S, Volberg A. The Tb-theorem on non-homogeneous spaces. Acta Math, 2003, 190:151- 239
[17]	Ouyang C, Xu Q. BMO functions and Carleson measures with values in uniformly convex spaces. Canad J Math, 2010, 62:827-844
[18]	Ouyang C, Yang W, Zhao R. Characterizations of Bergman spaces and Bloch space in the unit ball of Cn. Trans Amer Math Soc, 1995, 347:4301-4313
[19]	Pau J, Zhao R. Carleson measures and Toeplitz operators for weighted Bergman spaces on the unit ball. Michigan Math J, 2015, 64:759-796
[20]	Peng R, Ouyang C. Carleson measures for Besov-Sobolev spaces with applications in the unit ball of Cn. Acta Math Sci, 2013, 33B:1219-1230
[21]	Volberg A, Wick B D. Bergman-type singular integral operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball. Amer J Math, 2012, 134:949-992
[22]	Zhu K. Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics, Vol 226. New York:Springer-Verlag, 2005

SOME QUESTIONS REGARDING VERIFICATION OF CARLESON MEASURES

SOME QUESTIONS REGARDING VERIFICATION OF CARLESON MEASURES

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