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Winter 2015 Boundedness of a family of Hilbert-type operators and its Bergman-type analogue
Justice S. Bansah, Benoît F. Sehba
Illinois J. Math. 59(4): 949-977 (Winter 2015). DOI: 10.1215/ijm/1488186016

Abstract

In this paper, we first consider boundedness properties of a family of operators generalizing the Hilbert operator in the upper triangle case. In the diagonal case, we give the exact norm of these operators under some restrictions on the parameters. Second, we consider boundedness properties of a family of positive Bergman-type operators of the upper-half plane. We give necessary and sufficient conditions on the parameters under which these operators are bounded in the upper triangle case.

Citation

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Justice S. Bansah. Benoît F. Sehba. "Boundedness of a family of Hilbert-type operators and its Bergman-type analogue." Illinois J. Math. 59 (4) 949 - 977, Winter 2015. https://doi.org/10.1215/ijm/1488186016

Information

Received: 7 January 2016; Revised: 23 June 2016; Published: Winter 2015
First available in Project Euclid: 27 February 2017

zbMATH: 1370.47029
MathSciNet: MR3628296
Digital Object Identifier: 10.1215/ijm/1488186016

Subjects:
Primary: 26D15, 47B34
Secondary: 28A25

Rights: Copyright © 2015 University of Illinois at Urbana-Champaign

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Vol.59 • No. 4 • Winter 2015
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