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Toeplitz Operators on Dirichlet-Type Space of Unit Ball

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  • Jin Xia
  • Xiaofeng Wang
  • Guangfu Cao

Abstract

We construct a function in which is unbounded on any neighborhood of each boundary point of such that Toeplitz operator is a Schatten -class operator on Dirichlet-type space . Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type space . 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 is studied, where , , and is a radial function.

Suggested Citation

  • Jin Xia & Xiaofeng Wang & Guangfu Cao, 2014. "Toeplitz Operators on Dirichlet-Type Space of Unit Ball," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, June.
    • Handle: RePEc:hin:jnlaaa:927513
    DOI: 10.1155/2014/927513
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