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《ACTA ANALYSIS FUNCTIONALIS APPLICATA》 1999-01
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Schatten Class of Composition Operators on Weighted Dirichlet Spaces

XU Xian-min (Department of Mathematics, Zhejiang Normal University Jinhua 431004, China)  
In this paper, we characterize bounded, compact and Schatten class composition operators on weighted Dirichlet spaces. The method involves integral averages of the determining function of the operator, and the connection between composition operators on Dirichlet spaces and Toeplitz operators on Bergman spaces. The main result is as following: If p0,α>-1, and αε D_α(α-1), then C_ψbelongs to S_p(D_α) if and only if there is a constant δ0 such that the integral averages Φ_δ of τψ,α defined by belongs to L_2~p (dv). Where D(z,δ) is a pseudohyperbolic disk, τψ,α is the determining function for C_ψon D_α and dv (z) = (1 -|z|~2) ~-2dλ(z).
【Fund】: 浙江师范大学重点学科基金
【CateGory Index】: O177
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【Citations】
Chinese Journal Full-text Database 2 Hits
1 Xu Xianmin(Zhejiang Normal University);COMPOSITE OPERATORS ON THE WEIGHTED DIRICHLET SPACES[J];JOURNAL OF MATHEMATICS;1994-02
2 Xu Xianmin;Composition Operators on The Bergman Spaces[J];Journal of Zhejiang Normal University(Natural Sciences);1988-02
【Co-citations】
Chinese Journal Full-text Database 3 Hits
1 ~1Yu Yanyan ~2Liu Yongmin (1 School of Mathematics and Physics Science,Xuzhou Institute of Technology,Jiangsu Xuzhou 221008; 2 Department of Mathematics,Xuzhou Normal University,Jiangsu Xuzhou 221116);Composition Operators from Hyperbolicα-Bloch Spaces into Hyperbolic Q_K Type Spaces[J];Acta Mathematica Scientia;2009-05
2 CHEN Yong (College of Science, Zhejiang Normal University, Jinhua Zhejiang 321004);Composite Operator in the Weighted Dirichlet Spaces[J];Journal of Jiaxing College;2005-06
3 CHEN Yong (College of Mathematics,Physics and Information Science,Zhejiang Normal University,Jinhua Zhejiang 321004,China);Compact composition operators on weighted Dirichlet-type spaces[J];Journal of Zhejiang Normal University(Natoral Sciences);2002-03
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