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October 2020 On a Hilbert-type inequality with homogeneous kernel involving hyperbolic functions
Minghui You, Yue Guan
Rocky Mountain J. Math. 50(5): 1871-1881 (October 2020). DOI: 10.1216/rmj.2020.50.1871

Abstract

We first establish a Hilbert-type inequality and its equivalent Hardy form with best possible constant factors by constructing a homogeneous kernel function involving hyperbolic functions. Furthermore, we introduce Bernoulli numbers and the partial fraction expansions of trigonometric functions, and then we present several special and interesting Hilbert-type inequalities, in which the constant factors are represented by Bernoulli numbers and by some higher derivatives of trigonometric functions.

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Minghui You. Yue Guan. "On a Hilbert-type inequality with homogeneous kernel involving hyperbolic functions." Rocky Mountain J. Math. 50 (5) 1871 - 1881, October 2020. https://doi.org/10.1216/rmj.2020.50.1871

Information

Received: 6 October 2019; Accepted: 2 March 2020; Published: October 2020
First available in Project Euclid: 5 November 2020

zbMATH: 07274843
MathSciNet: MR4170695
Digital Object Identifier: 10.1216/rmj.2020.50.1871

Subjects:
Primary: 26D15, 41A17

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 5 • October 2020
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