Acta mathematica scientia, Series B >
THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL
Received date: 2015-09-02
Online published: 2017-04-25
Supported by
The research is supported by the National Natural Science Foundation of China (11571104) and Hunan Provincial Natural Science Foundation of China (2015JJ2095)
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 Tφ,ψ from the μ-Bergman space Ap(μ) to the normal weight Bloch type space βν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator Cφ is compact from Ap(μ) to βν is given. At the same time, the authors give the briefly sufficient and necessary condition that Cφ is compact on βu 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 . DOI: 10.1016/S0252-9602(17)30012-7
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