On a Half-Discrete Hilbert-Type Inequality in the Whole Plane with the Kernel of Hyperbolic Secant Function Related to the Hurwitz Zeta Function

Michael Th. Rassias (), Bicheng Yang () and Andrei Raigorodskii ()
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Michael Th. Rassias: University of Zurich, Institute of Mathematics
Bicheng Yang: Guangdong University of Education, Department of Mathematics
Andrei Raigorodskii: Moscow Institute of Physics and Technology

A chapter in Trigonometric Sums and Their Applications, 2020, pp 229-259 from Springer

Abstract: Abstract Using weight functions, we obtain a half-discrete Hilbert-type inequality in the whole plane with the kernel of hyperbolic secant function and multi-parameters. The constant factor related to the Hurwitz zeta function is proved to be the best possible. We also consider equivalent forms, two kinds of particular inequalities, the operator expressions and some reverses.

Keywords: Half-discrete Hilbert-type inequality; Weight function; Equivalent form; Operator expression; Hurwitz zeta function; 26D15; 30A10; 47A05 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-37904-9_11

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DOI: 10.1007/978-3-030-37904-9_11

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