Carleson Measures and Toeplitz Operators on Small Bergman Spaces on the Ball

被引：1
|
作者：
Le, Van An [1 ,2 ]
机构：
[1] Aix Marseille Univ, CNRS, Cent Marseille, I2M, Marseille, France
[2] Univ Quynhon, Dept Math & Stat, 170 An Duong Vuong, Quy Nhon, Vietnam
来源：
CZECHOSLOVAK MATHEMATICAL JOURNAL | 2021年 / 71卷 / 01期
关键词：
Bergman space; Carleson measure; Toeplitz operator; Schatten classes; TRACE IDEAL CRITERIA;
D O I：
10.21136/CMJ.2020.0265-19
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study Carleson measures and Toeplitz operators on the class of so-called small weighted Bergman spaces, introduced recently by Seip. A characterization of Carleson measures is obtained which extends Seip's results from the unit disk of DOUBLE-STRUCK CAPITAL C to the unit ball of DOUBLE-STRUCK CAPITAL C-n. We use this characterization to give necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators. Finally, we study the Schatten p classes membership of Toeplitz operators for 1 < p < infinity.
引用
收藏
页码：211 / 229
页数：19
相关论文
共 50 条
  • [41] Toeplitz Operators on Weighted Bergman Spaces
    Chacon, Gerardo R.
    JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2013,
  • [42] TOEPLITZ-OPERATORS ON BERGMAN SPACES
    ZENG, XF
    HOUSTON JOURNAL OF MATHEMATICS, 1992, 18 (03): : 387 - 407
  • [43] Toeplitz Operators on Generalized Bergman Spaces
    Chailuek, Kamthorn
    Hall, Brian C.
    INTEGRAL EQUATIONS AND OPERATOR THEORY, 2010, 66 (01) : 53 - 77
  • [44] Toeplitz Operators on Generalized Bergman Spaces
    Kamthorn Chailuek
    Brian C. Hall
    Integral Equations and Operator Theory, 2010, 66 : 53 - 77
  • [45] Carleson Measures for Variable Exponent Bergman Spaces
    Gerardo R. Chacón
    Humberto Rafeiro
    Juan Camilo Vallejo
    Complex Analysis and Operator Theory, 2017, 11 : 1623 - 1638
  • [46] Toeplitz operators on Bergman spaces induced by doubling weights in the unit ball of Cn
    Du, Juntao
    Hu, Bingyang
    Li, Songxiao
    Zhou, Xiaojing
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 544 (02)
  • [47] The Essential Norm of Toeplitz Operators Between Bergman Spaces of the Unit Ball in Cn
    Luo, Luo
    COMPLEX ANALYSIS AND OPERATOR THEORY, 2015, 9 (02) : 265 - 273
  • [48] A TECHNIQUE FOR CHARACTERIZING CARLESON MEASURES ON BERGMAN SPACES
    LUECKING, D
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 87 (04) : 656 - 660
  • [49] Carleson Measures for Variable Exponent Bergman Spaces
    Chacon, Gerardo R.
    Rafeiro, Humberto
    Camilo Vallejo, Juan
    COMPLEX ANALYSIS AND OPERATOR THEORY, 2017, 11 (07) : 1623 - 1638
  • [50] Φ-CARLESON MEASURES AND MULTIPLIERS BETWEEN BERGMAN-ORLICZ SPACES OF THE UNIT BALL OF Cn
    Sehba, Benoit F.
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2018, 104 (01) : 63 - 79
12345