A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function
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摘要
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.
论文关键词：Gamma function,Riemann zeta function,Numerical estimates,Half-discrete Hilbert’s inequality,Weight function,Hermite–Hadamard’s inequality,Hilbert’s operator,Equivalent form
论文评审过程：Available online 18 October 2013.
论文官网地址：https://doi.org/10.1016/j.amc.2013.09.040
