A Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums

Bicheng Yang, Shanhe Wu and Xingshou Huang
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Bicheng Yang: Institute of Applied Mathematics, Longyan University, Longyan 364012, China
Shanhe Wu: Department of Mathematics, Longyan University, Longyan 364012, China
Xingshou Huang: School of Mathematics and Statistics, Hechi University, Yizhou 456300, China

Mathematics, 2021, vol. 9, issue 22, 1-15

Abstract: In this paper, we establish a new Hardy–Hilbert-type inequality involving parameters composed of a pair of weight coefficients with their sum. Our result is a unified generalization of some Hardy–Hilbert-type inequalities presented in earlier papers. Based on the obtained inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed, and the equivalent forms and the operator expressions are also considered. As applications, we illustrate how the inequality obtained can generate some new Hardy–Hilbert-type inequalities.

Keywords: weight coefficients; Hardy–Hilbert-type inequality; Euler–Maclaurin summation formula; equivalent conditions; operator expressions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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