A Hilbert-Type Integral Inequality in the Whole Plane Related to the Hypergeometric Function and the Beta Function

2015/12/15 by Michael Th. Rassias, Rassias, Michael Th., Bicheng Yang +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1512.04706

openalex publication_date 2015/12/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A new Hilbert-type integral inequality in the whole plane with the non-homogeneous kernel and parameters is given. The constant factor related to the hypergeometric function and the beta function is proved to be the best possible. As applications, equivalent forms, the reverses, some particular examples, two kinds of Hardy-type inequalities, and operator expressions are considered.

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