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Bounded Hankel Products on the Bergman Space of the Polydisk

Part of: Special classes of linear operators

Published online by Cambridge University Press:  20 November 2018

Yufeng Lu  and
Shuxia Shang
Yufeng Lu
Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China, [email protected]@163.com
Shuxia Shang
Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China, [email protected]@163.com
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Abstract

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We consider the problem of determining for which square integrable functions $f$ and $g$ on the polydisk the densely defined Hankel product ${{H}_{f}}\,H_{g}^{*}$ is bounded on the Bergman space of the polydisk. Furthermore, we obtain similar results for the mixed Haplitz products ${{H}_{g}}\,{{T}_{{\bar{f}}}}$ and ${{T}_{f}}\,H_{g}^{*}$, where $f$ and $g$ are square integrable on the polydisk and $f$ is analytic.

Keywords

Toeplitz operatorHankel operatorHaplitz productsBergman spacepolydisk

MSC classification

Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Secondary: 47B47: Commutators, derivations, elementary operators, etc.
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 1 , 01 February 2009 , pp. 190 - 204
Copyright
Copyright © Canadian Mathematical Society 2009

References

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