Products of Hankel and Toeplitz Operators on the Bergman Space

Karel Stroethoff; Dechao Zheng

doi:10.1006/jfan.1999.3489

Products of Hankel and Toeplitz Operators on the Bergman Space

Karel Stroethoff
, Dechao Zheng

Mathematical Sciences

Vanderbilt University

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

55 Scopus citations

Abstract

We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products T_fT_g are bounded on the Bergman space. We prove results analogous to those obtained by the second author [17] for such Toeplitz products on the Hardy space. We furthermore obtain similar results for Hankel products H_fH*_g, where f and g are square integrable on the unit disk, and for the mixed Haplitz products H_fT_g and T_gH*_f, where f and g are square integrable on the unit disk and g is analytic.

Original language	English
Pages (from-to)	289-313
Number of pages	25
Journal	Journal of Functional Analysis
Volume	169
Issue number	1
DOIs	https://doi.org/10.1006/jfan.1999.3489
State	Published - Dec 1 1999

Funding

1Supported in part by the National Science Foundation and University Research Council of Vanderbilt University.

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abstract = "We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products TfTg are bounded on the Bergman space. We prove results analogous to those obtained by the second author [17] for such Toeplitz products on the Hardy space. We furthermore obtain similar results for Hankel products HfH*g, where f and g are square integrable on the unit disk, and for the mixed Haplitz products HfTg and TgH*f, where f and g are square integrable on the unit disk and g is analytic.",

author = "Karel Stroethoff and Dechao Zheng",

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AU - Zheng, Dechao

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N2 - We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products TfTg are bounded on the Bergman space. We prove results analogous to those obtained by the second author [17] for such Toeplitz products on the Hardy space. We furthermore obtain similar results for Hankel products HfH*g, where f and g are square integrable on the unit disk, and for the mixed Haplitz products HfTg and TgH*f, where f and g are square integrable on the unit disk and g is analytic.

AB - We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products TfTg are bounded on the Bergman space. We prove results analogous to those obtained by the second author [17] for such Toeplitz products on the Hardy space. We furthermore obtain similar results for Hankel products HfH*g, where f and g are square integrable on the unit disk, and for the mixed Haplitz products HfTg and TgH*f, where f and g are square integrable on the unit disk and g is analytic.

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Products of Hankel and Toeplitz Operators on the Bergman Space

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