Schatten-Herz class Toeplitz operators on harmonic Bergman spaces of smooth domains in Rn

Authors

  • Xiaofen Lv,

    Corresponding author
    1. College of Mathematics and Science, Xiamen University, Xiamen, Fujian, 361005, P. R. China. Phone: +86 572 232 1163, Fax: +86 572 232 1163
    • College of Mathematics and Science, Xiamen University, Xiamen, Fujian, 361005, P. R. China, Phone: +86 572 232 1163, Fax: +86 572 232 1163
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  • Zhangjian Hu

    1. Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang, 313000, P. R. China. Phone: +86 572 232 1055, Fax: +86 572 232 1059
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Abstract

On the setting of the bounded domain Ω in equation image with C boundary, we introduce the Schatten-Herz classes Toeplitz operators. And in term of averaging functions and Berezin transforms, we characterize those finite positive Borel measures μ on Ω for which the induced Toeplitz operators are in Shatten-Herz classes. As some preliminary results, we obtain the sharp estimate of integral means for the harmonic Bergman kernel on the level surface and the boundedness of the Berezin transform on the Herz spaces.

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