Composition Operators on the Bergman Space with Quasiconformal Symbols

被引：0

作者：

Fang, Xiang ^{[1
]}

Guo, Kunyu ^{[2
]}

Wang, Zipeng ^{[3
]}

机构：

[1] Natl Cent Univ, Dept Math, Chungli, Taiwan

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2023年 / 33卷 / 04期

关键词：

Composition operator; Bergman space; Quasiconformal mapping; Carleson box; SMOOTH SELF-MAPS; BOUNDARY CORRESPONDENCE; MEAN-OSCILLATION; INEQUALITIES; MAPPINGS; THEOREMS; BMO; HOMEOMORPHISMS; DISTORTION; NORM;

D O I：

10.1007/s12220-022-01172-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper introduces and studies composition operators on the Bergman space with quasiconformal symbols. We first characterize the boundedness of the norms. Then we discuss operator-theoretic issues including compactness characterization, essential norms, Schatten class membership, and conditions for closed ranges.

引用

页数：38

共 50 条

[1] Composition Operators on the Bergman Space with Quasiconformal Symbols
Xiang Fang
Kunyu Guo
Zipeng Wang
[J]. The Journal of Geometric Analysis, 2023, 33
[2] Continuity with respect to symbols of composition operators on the weighted Bergman space
Stevic, Stevo
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2007, 11 (04): : 1177 - 1188
[3] SELF-COMMUTATORS OF COMPOSITION OPERATORS WITH MONOMIAL SYMBOLS ON THE BERGMAN SPACE
Abdollahi, A.
Mehrangiz, S.
Roientan, T.
[J]. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2015, 41 (07): : 65 - 76
[4] COMPOSITION OPERATORS ON BERGMAN SPACE
BOYD, DM
[J]. COLLOQUIUM MATHEMATICUM, 1975, 34 (01) : 127 - 136
[5] Characterizations of Bergman space Toeplitz operators with harmonic symbols
Louhichi, Issam
Olofsson, Anders
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2008, 617 : 1 - 26
[6] Subnormality and composition operators on the Bergman space
Richman, AE
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2003, 45 (01) : 105 - 124
[7] Weighted composition operators on the Bergman space
Cuckovic, Z
Zhao, RH
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2004, 70 : 499 - 511
[8] Subnormality and composition operators on the Bergman space
Alexander E. Richman
[J]. Integral Equations and Operator Theory, 2003, 45 : 105 - 124
[9] Hyponormality of Toeplitz operators with polynomial symbols on the weighted Bergman space
Phukon A.
[J]. Arabian Journal of Mathematics, 2017, 6 (2) : 87 - 94
[10] The Commutants of the Toeplitz Operators with Radial Symbols on the Pluriharmonic Bergman Space
Jun YANG
[J]. Journal of Mathematical Research with Applications, 2015, 35 (01) : 110 - 118

← 1 2 3 4 5 →