Acta mathematica scientia, Series B >
COMPACT COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES ON BOUNDED SYMMETRIC DOMAINS
Received date: 2008-10-14
Online published: 2011-03-20
Supported by
Supported by the National Natural Science Foundation of China (10771064), Natural Science Foundation of Zhejiang Province (Y7080197, Y6090036, Y6100219), Foundation of Creative Group in Colleges and Universities of Zhejiang Province (T200924), and Foundation of Department of Education of Zhejiang province (20070482)
In this article, we borrow the idea of using Schur's test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetric domain Ω, and verify that Cφ is compact on Lqa(Ω, dvβ) if and only if K(φ(z), φ(z))/K(z, z)→0 as z→∂Ω under a mild condition, where K(z, w) is the Bergman kernel.
LV Xiao-Fen , HU Zhang-Jian . COMPACT COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES ON BOUNDED SYMMETRIC DOMAINS[J]. Acta mathematica scientia, Series B, 2011 , 31(2) : 468 -476 . DOI: 10.1016/S0252-9602(11)60247-6
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