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May 2018 Equivalent properties of a Hilbert-type integral inequality with the best constant factor related to the Hurwitz zeta function
Michael Rassias, Bicheng Yang
Ann. Funct. Anal. 9(2): 282-295 (May 2018). DOI: 10.1215/20088752-2017-0031

Abstract

By the use of methods of real analysis and weight functions, we study the equivalent properties of a Hilbert-type integral inequality with the nonhomogeneous kernel. The constant factor related to the Hurwitz zeta function is proved to be the best possible. As a corollary, a few equivalent conditions of a Hilbert-type integral inequality with the homogeneous kernel are deduced. We also consider their operator expressions.

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Michael Rassias. Bicheng Yang. "Equivalent properties of a Hilbert-type integral inequality with the best constant factor related to the Hurwitz zeta function." Ann. Funct. Anal. 9 (2) 282 - 295, May 2018. https://doi.org/10.1215/20088752-2017-0031

Information

Received: 2 April 2017; Accepted: 18 June 2017; Published: May 2018
First available in Project Euclid: 18 November 2017

zbMATH: 06873704
MathSciNet: MR3795092
Digital Object Identifier: 10.1215/20088752-2017-0031

Subjects:
Primary: 26D15
Secondary: 65B10

Keywords: ‎equivalent ‎form , Hilbert-type integral inequality , Hurwitz zeta function , operator , ‎weight function

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 2 • May 2018
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