On a multidimensional half-discrete Hilbert-type inequality related to the hyperbolic cotangent function

Abstract

In this paper, by the application of methods of weight functions and the use of analytic techniques, a multidimensional more accurate half-discrete Hilbert-type inequality with the kernel of the hyperbolic cotangent function is proved. We show that the constant factor related to the Riemann zeta function is the best possible. Equivalent forms as well as operator expressions are also investigated.