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A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
225
Identifiers
DOI: 10.1016/j.amc.2013.09.040
Keywords
  • Gamma Function
  • Riemann Zeta Function
  • Numerical Estimates
  • Half-Discrete Hilbert’S Inequality
  • Weight Function
  • Hermite–Hadamard’S Inequality
  • Hilbert’S Operator
  • Equivalent Form
Disciplines
  • Mathematics

Abstract

Abstract In this paper, by applying methods of weight functions and techniques of real analysis, a more accurate multidimensional half-discrete Hilbert’s inequality with the best possible constant factor related to the Riemann zeta function is proved. Equivalent forms and some reverses are also obtained. Additionally, we consider the operator expressions with the norms and finally present a corollary related to the non-homogeneous kernel.

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