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

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

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (2): 425-438.doi: 10.1016/S0252-9602(17)30012-7

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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)

Abstract

Abstract:

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.

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

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.

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

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