Bounded Toeplitz products on Bergman spaces of the unit ball

Karel Stroethoff; Dechao Zheng

doi:10.1016/j.jmaa.2006.01.009

Bounded Toeplitz products on Bergman spaces of the unit ball

Karel Stroethoff
, Dechao Zheng

Mathematical Sciences

Vanderbilt University

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We consider the question for which square integrable analytic functions f and g on the unit ball the densely defined products T_f T_{over(g, ̄)} are bounded on the weighted Bergman spaces. We prove results analogous to those we obtained in the setting of the unit disk and the polydisk.

Original language	English
Pages (from-to)	114-129
Number of pages	16
Journal	Journal of Mathematical Analysis and Applications
Volume	325
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2006.01.009
State	Published - Jan 1 2007

Funding

* Corresponding author. E-mail addresses: [email protected] (K. Stroethoff), [email protected] (D. Zheng). 1 Partially supported by the National Science Foundation.

Keywords

Bergman spaces
Toeplitz operator
Unit ball

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10.1016/j.jmaa.2006.01.009

Cite this

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title = "Bounded Toeplitz products on Bergman spaces of the unit ball",

abstract = "We consider the question for which square integrable analytic functions f and g on the unit ball the densely defined products Tf Tover(g,{\= }) are bounded on the weighted Bergman spaces. We prove results analogous to those we obtained in the setting of the unit disk and the polydisk.",

keywords = "Bergman spaces, Toeplitz operator, Unit ball",

author = "Karel Stroethoff and Dechao Zheng",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (K. Stroethoff), [email protected] (D. Zheng). 1 Partially supported by the National Science Foundation.",

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AU - Zheng, Dechao

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PY - 2007/1/1

Y1 - 2007/1/1

N2 - We consider the question for which square integrable analytic functions f and g on the unit ball the densely defined products Tf Tover(g, ̄) are bounded on the weighted Bergman spaces. We prove results analogous to those we obtained in the setting of the unit disk and the polydisk.

AB - We consider the question for which square integrable analytic functions f and g on the unit ball the densely defined products Tf Tover(g, ̄) are bounded on the weighted Bergman spaces. We prove results analogous to those we obtained in the setting of the unit disk and the polydisk.

KW - Bergman spaces

KW - Toeplitz operator

KW - Unit ball

UR - https://www.scopus.com/pages/publications/33750360231

U2 - 10.1016/j.jmaa.2006.01.009

DO - 10.1016/j.jmaa.2006.01.009

M3 - Article

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EP - 129

JO - Journal of Mathematical Analysis and Applications

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IS - 1

ER -

Bounded Toeplitz products on Bergman spaces of the unit ball

Abstract

Funding

Keywords

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