数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 468-476.doi: 10.1016/S0252-9602(11)60247-6

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COMPACT COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES ON BOUNDED SYMMETRIC DOMAINS

吕小芬, 胡璋剑   

  1. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
  • 收稿日期:2008-10-14 出版日期:2011-03-20 发布日期:2011-03-20
  • 基金资助:

    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)

COMPACT COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES ON BOUNDED SYMMETRIC DOMAINS

 LV Xiao-Fen, HU Zhang-Jian   

  1. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
  • Received:2008-10-14 Online:2011-03-20 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)

摘要:

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.

关键词: Composition operator, weighted Bergman space, bounded symmetric domains

Abstract:

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.

Key words: Composition operator, weighted Bergman space, bounded symmetric domains

中图分类号: 

  • 47B38