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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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