A Multidimensional Hilbert-Type Integral Inequality Related to the Riemann Zeta Function

2013/08/06 by Michael Th. Rassias, Rassias, Michael Th., Bicheng Yang +1
Mathematics · #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1308.1264

arxiv created 2013/08/06 · openalex publication_date 2013/08/06 · arxiv updated 2013/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper,using methods of weight functions and techniques of real analysis, we provide a multidimensional Hilbert-type integral inequality with a homogeneous kernel of degree 0 as well as a best possible constant factor related to the Riemann zeta function. Some equivalent representations and certain reverses are obtained. Furthermore, we also consider operator expressions with the norm and some particular results.

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