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Schatten p-class Toeplitz operators with unbounded symbols on pluriharmonic Bergman space

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Abstract

In this paper, we construct the function u in L 2(\(\mathbb{B}_n \), dA) which is unbounded on any neighborhood of each boundary point of \(\mathbb{B}_n \) such that T u is the Schatten p-class (0 < p < ∞) operator on pluriharmonic Bergman space h 2(\(\mathbb{B}_n \), dA) for several complex variables. In addition, we also discuss the compactness of Toeplitz operators with L 1 symbols.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, 510006, P. R. China

    Xiao Feng Wang, Jin Xia & Guang Fu Cao

Authors
  1. Xiao Feng Wang
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  2. Jin Xia
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  3. Guang Fu Cao
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Correspondence to Jin Xia.

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Supported by National Natural Science Foundation of China (Grant No. 11271092)

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Wang, X.F., Xia, J. & Cao, G.F. Schatten p-class Toeplitz operators with unbounded symbols on pluriharmonic Bergman space. Acta. Math. Sin.-English Ser. 29, 2355–2366 (2013). https://doi.org/10.1007/s10114-013-1581-x

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  • DOI: https://doi.org/10.1007/s10114-013-1581-x

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