Illinois Journal of Mathematics

Boundedness of a family of Hilbert-type operators and its Bergman-type analogue

Justice S. Bansah and Benoît F. Sehba

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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.

Article information

Source
Illinois J. Math., Volume 59, Number 4 (2015), 949-977.

Dates
Received: 7 January 2016
Revised: 23 June 2016
First available in Project Euclid: 27 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1488186016

Digital Object Identifier
doi:10.1215/ijm/1488186016

Mathematical Reviews number (MathSciNet)
MR3628296

Zentralblatt MATH identifier
1370.47029

Subjects
Primary: 47B34: Kernel operators 26D15: Inequalities for sums, series and integrals
Secondary: 28A25: Integration with respect to measures and other set functions

Citation

Bansah, Justice S.; Sehba, Benoît F. Boundedness of a family of Hilbert-type operators and its Bergman-type analogue. Illinois J. Math. 59 (2015), no. 4, 949--977. doi:10.1215/ijm/1488186016. https://projecteuclid.org/euclid.ijm/1488186016


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References

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