THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

doi:10.1016/S0252-9602(17)30012-7

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (2): 425-438.doi: 10.1016/S0252-9602(17)30012-7

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

黎深莲, 张学军, 徐思

College of Mathematics and Computer Science, Hunan Normal University, Changsha 410006, China

收稿日期:2015-09-02 出版日期:2017-04-25 发布日期:2017-04-25
通讯作者: Xuejun ZHANG,E-mail:xuejunttt@263.net E-mail:xuejunttt@263.net
作者简介:Xuejun ZHANG,E-mail:xuejunttt@263.net
基金资助:
The research is supported by the National Natural Science Foundation of China (11571104) and Hunan Provincial Natural Science Foundation of China (2015JJ2095)

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

Shenlian LI, Xuejun ZHANG, Si XU

College of Mathematics and Computer Science, Hunan Normal University, Changsha 410006, China

Received:2015-09-02 Online:2017-04-25 Published:2017-04-25
Contact: Xuejun ZHANG,E-mail:xuejunttt@263.net E-mail:xuejunttt@263.net
Supported by:
The research is supported by the National Natural Science Foundation of China (11571104) and Hunan Provincial Natural Science Foundation of China (2015JJ2095)

摘要/Abstract

摘要：

Let p > 0 and μ be a normal function on[0,1), ν(r)=(1-r²)^1+(n/p) μ(r) for r ∈[0,1). In this article, the bounded or compact weighted composition operator T_φ,ψ from the μ-Bergman space A^p(μ) to the normal weight Bloch type space β_ν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator C_φ is compact from A^p(μ) to β_ν is given. At the same time, the authors give the briefly sufficient and necessary condition that C_φ is compact on β_u for a > 1.

关键词: u-Bergman space, u-Bloch space, composition operator, compactness

Abstract:

Key words: u-Bergman space, u-Bloch space, composition operator, compactness

黎深莲, 张学军, 徐思. THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL[J]. 数学物理学报(英文版), 2017, 37(2): 425-438.

Shenlian LI, Xuejun ZHANG, Si XU. THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL[J]. Acta mathematica scientia,Series B, 2017, 37(2): 425-438.

[1]	Jasbir Singh MANHAS, Ruhan ZHAO. PRODUCTS OF WEIGHTED COMPOSITION AND DIFFERENTIATION OPERATORS INTO WEIGHTED ZYGMUND AND BLOCH SPACES[J]. 数学物理学报(英文版), 2018, 38(4): 1105-1120.
[2]	王茂发, 姚兴兴, 邓方文. WEIGHTED COMPOSITION OPERATORS ON THE HILBERT SPACE OF DIRICHLET SERIES[J]. 数学物理学报(英文版), 2018, 38(4): 1427-1440.
[3]	刘树君, 陈芳启, 王泽军. EXISTENCE OF GLOBAL L^∞ SOLUTIONS TO A GENERALIZED n×n HYPERBOLIC SYSTEM OF LEROUX TYPE[J]. 数学物理学报(英文版), 2018, 38(3): 889-897.
[4]	刘春燕, 张子厚, 周宇. A NOTE IN APPROXIMATIVE COMPACTNESS AND MIDPOINT LOCALLY K-UNIFORM ROTUNDITY IN BANACH SPACES[J]. 数学物理学报(英文版), 2018, 38(2): 643-650.
[5]	Van Hien LE, Dinh Ke TRAN, Trong Kinh CHU. GLOBALLY ATTRACTING SOLUTIONS TO IMPULSIVE FRACTIONAL DIFFERENTIAL INCLUSIONS OF SOBOLEV TYPE[J]. 数学物理学报(英文版), 2017, 37(5): 1295-1318.
[6]	Juan J. NIETO, Bessem SAMET. SOLVABILITY OF AN IMPLICIT FRACTIONAL INTEGRAL EQUATION VIA A MEASURE OF NONCOMPACTNESS ARGUMENT[J]. 数学物理学报(英文版), 2017, 37(1): 195-204.
[7]	Mohamed BEN AYED, Habib FOURTI. SCALAR CURVATURE TYPE PROBLEM ON THE THREE DIMENSIONAL BOUNDED DOMAIN[J]. 数学物理学报(英文版), 2017, 37(1): 139-173.
[8]	Sanjukta DAS, Dwijendra PANDEY, N. SUKAVANAM. EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY[J]. 数学物理学报(英文版), 2016, 36(5): 1509-1523.
[9]	曹文涛, 黄飞敏, 李天虹, 于慧敏. GLOBAL ENTROPY SOLUTIONS TO AN INHOMOGENEOUS ISENTROPIC COMPRESSIBLE EULER SYSTEM[J]. 数学物理学报(英文版), 2016, 36(4): 1215-1224.
[10]	Jasbir Singh MANHAS, Ruhan ZHAO. ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS[J]. 数学物理学报(英文版), 2015, 35(6): 1401-1410.
[11]	A. AGHAJANI, M. MURSALEEN, A. SHOLE HAGHIGHI. FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS[J]. 数学物理学报(英文版), 2015, 35(3): 552-566.
[12]	D. SENTHILKUMAR, P. CHANDRA KALA. TENSOR SUM AND DYNAMICAL SYSTEMS[J]. 数学物理学报(英文版), 2014, 34(6): 1935-1946.
[13]	陈志华, 江良美, 颜启明. AN UPPER BOUND OF THE ESSENTIAL NORM OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES[J]. 数学物理学报(英文版), 2014, 34(4): 1145-1156.
[14]	Afif BEN AMAR. THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND (ws)-COMPACT OPERATORS[J]. 数学物理学报(英文版), 2014, 34(2): 263-273.
[15]	Bilel KRICHEN. RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS[J]. 数学物理学报(英文版), 2014, 34(2): 546-556.

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0