A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function

Author:

You Minghui

Abstract

AbstractIn this work, by the introduction of some parameters, a new half-discrete kernel function in the whole plane is defined, which involves both the homogeneous and the nonhomogeneous cases. By employing some techniques of real analysis, especially the method of a weight function, a new half-discrete Hilbert-type inequality with the new kernel function, as well as its equivalent Hardy-type inequalities are established. Moreover, it is proved that the constant factors of the newly obtained inequalities are the best possible. Finally, assigning special values to the parameters, some new half-discrete Hilbert-type inequalities with special kernels are presented at the end of the paper.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference32 articles.

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