DK SPACES AND CARLESON MEASURES

doi:10.1007/s10473-022-0316-4

Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (3): 1103-1112.doi: 10.1007/s10473-022-0316-4

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D_K SPACES AND CARLESON MEASURES

Dongxing LI¹, Hasi WULAN², Ruhan ZHAO³

1. School of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou, 510521, China;
2. Department of Mathematics, Shantou University, Shantou, 515063, China;
3. Department of Mathematics, SUNY Brockport, Brockport, NY, 14420, USA

Received:2020-12-09 Revised:2021-07-31 Published:2022-06-24
Contact: Ruhan ZHAO,E-mail:rzhao@brockport.edu E-mail:rzhao@brockport.edu
Supported by:
This research is supported by the China National Natural Science Foundation (11720101003).

Abstract

CLC Number:

46E15

Dongxing LI, Hasi WULAN, Ruhan ZHAO. D_K SPACES AND CARLESON MEASURES[J].Acta mathematica scientia,Series B, 2022, 42(3): 1103-1112.

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[1] Aleman A, Carlsson M, Persson A. Preduals of Q_p-spaces II. Carleson imbeddings and atomic decompositions. Comp Var Ellip Eq, 2007, 52:629-653
[2] Arcozzi N, Rochberg R, Sawyer E. Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls. Adv Math, 2008, 218:1107-1180
[3] Arcozzi N, Rochberg R, Sawyer E, Wick B D. The Dirichlet space and related function spaces. Providence, RI:American Math Soc, 2019
[4] Aulaskari R, Girela D, Wulan H. Q_p spaces, Hadamard products and Carleson measures. Math Reports, 2000, 2(52):421-430
[5] Aulaskari R, Xiao J, Zhao R. On subspaces and subsets of BMOA and UBC. Analysis, 1995, 15:101-121
[6] Aulaskari R, Stegenga D, Xiao J. Some subclasses of BMOA and their characterization in terms of Carleson measures. Rocky Mountain J Math, 1996, 26:485-506
[7] Bao G, Wulan H. Q_K spaces:a brief and selective survey. Acta Mathematica Scientia, 2021, 41B(6):2039-2054
[8] Carleson L. Interpolations by bounded analytic functions and the corona problem. Ann Math, 1962, 76:547-559
[9] Essén M, Wulan H. Carleson type measures and their applications. Complex Variables, 2000, 42:67-88
[10] Essén E, Wulan H. On analytic and meromorphic functions and spaces of Q_K type. Illinois J Math, 2002, 46:1233-1258
[11] Essén M, Wulan H, Xiao J. Several function-theoretic characterizations of Möbius invariant Q_K spaces. J Funct Anal, 2006, 230:78-115
[12] El-Fallah O, Kellay K, Mashreghi J, Ransford T. One-box conditions for Carleson measures for the Dirichlet space. Proc Amer Math Soc, 2015, 143:679-684
[13] Oleinik V. Embedding theorems for weighted classes of harmonic and analytic functions (in Russian). Zap Nauch Sem LOMI Steklov, 1974, 47:120-137; Translation in J Soviet Math, 1978, 9:228-243
[14] Pau J, Peláez J A. Multipliers of Möbius invariant Q_s space. Math Z, 2009, 261:545-555
[15] Stegenga D. Multipliers of the Dirichlet space. Illinois J Math, 1980, 24:113-139
[16] Wu Z. Carleson measures and multipliers for Dirichlet spaces. J Funct Anal, 1999, 169:148-163
[17] Wulan H, Zhu K. Lacunary series in Q_K spaces. Studia Math, 2007, 178:217-230
[18] Wulan H, Zhu K. Möbius Invariant Q_K Spaces. Cham:Springer, 2017
[19] Wulan H. Criteria for an analytic function belonging to Q_K spaces. Acta Mathematica Scientia, 2009, 29B(1):33-44
[20] Zhao R. On F(p, q, s) spaces. Acta Mathematica Scientia, 2021, 41B(6):1985-2020

D_K SPACES AND CARLESON MEASURES

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