, Volume 29, Issue 12, pp 2355-2366
Date: 20 Feb 2013

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.

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