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2014 Toeplitz Operators on Dirichlet-Type Space of Unit Ball
Jin Xia, Xiaofeng Wang, Guangfu Cao
Abstr. Appl. Anal. 2014: 1-13 (2014). DOI: 10.1155/2014/927513


We construct a function u in L2Bn, dV which is unbounded on any neighborhood of each boundary point of Bn such that Toeplitz operator Tu is a Schatten p-class 0<p< operator on Dirichlet-type space DBn, dV. Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type space DBn, dV. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. We investigate the zero-product problem for several Toeplitz operators with radial symbols. Furthermore, the corresponding commuting problem of Toeplitz operators whose symbols are of the form ξku is studied, where kZn, ξBn, and u is a radial function.


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Jin Xia. Xiaofeng Wang. Guangfu Cao. "Toeplitz Operators on Dirichlet-Type Space of Unit Ball." Abstr. Appl. Anal. 2014 1 - 13, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023326
MathSciNet: MR3228097
Digital Object Identifier: 10.1155/2014/927513

Rights: Copyright © 2014 Hindawi


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