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On a Hilbert-Type Integral Inequality Related to the Extended Hurwitz Zeta Function in the Whole Plane

On a Hilbert-Type Integral Inequality Related to the Extended Hurwitz Zeta Function in the Whole... By using techniques of real analysis and weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related the extended Hurwitz zeta function is proved to be the best possible. As applications, a few equivalent statements of a Hilbert-type integral inequality with the homogeneous kernel in the whole plane are deduced. We also consider the operator expressions and some corollaries. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

On a Hilbert-Type Integral Inequality Related to the Extended Hurwitz Zeta Function in the Whole Plane

Acta Applicandae Mathematicae , Volume 160 (1) – Jun 14, 2018

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References (40)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Nature B.V.
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-018-0195-9
Publisher site
See Article on Publisher Site

Abstract

By using techniques of real analysis and weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related the extended Hurwitz zeta function is proved to be the best possible. As applications, a few equivalent statements of a Hilbert-type integral inequality with the homogeneous kernel in the whole plane are deduced. We also consider the operator expressions and some corollaries.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Jun 14, 2018

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