Articles

DK SPACES AND CARLESON MEASURES

  • Dongxing LI ,
  • Hasi WULAN ,
  • Ruhan ZHAO
Expand
  • 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 date: 2020-12-09

  Revised date: 2021-07-31

  Online published: 2022-06-24

Supported by

This research is supported by the China National Natural Science Foundation (11720101003).

Abstract

We give some characterizations of Carleson measures for Dirichlet type spaces by using Hadamard products. We also give a one-box condition for such Carleson measures.

Cite this article

Dongxing LI , Hasi WULAN , Ruhan ZHAO . DK SPACES AND CARLESON MEASURES[J]. Acta mathematica scientia, Series B, 2022 , 42(3) : 1103 -1112 . DOI: 10.1007/s10473-022-0316-4

References

[1] Aleman A, Carlsson M, Persson A. Preduals of Qp-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. Qp 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. QK 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 QK type. Illinois J Math, 2002, 46:1233-1258
[11] Essén M, Wulan H, Xiao J. Several function-theoretic characterizations of Möbius invariant QK 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 Qs 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 QK spaces. Studia Math, 2007, 178:217-230
[18] Wulan H, Zhu K. Möbius Invariant QK Spaces. Cham:Springer, 2017
[19] Wulan H. Criteria for an analytic function belonging to QK 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
Options
Outlines

/