Discrete Hilbert-Type Inequalities

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Discrete Hilbert-type inequalities including Hilbert's inequality are important in mathematical analysis and its applications. In 1998, the author presented an extension of Hilbert's integral ...
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Some Innovative Hilbert-Type Inequalities

Pp. 90-121 (32)

Bicheng Yang

Abstract

In this chapter, based on some theorems of Chapter 4, by using the technique of r eal analysis and applying the improved Euler-Macraurin’s summation formula mentioned in Chapter 2, we discuss how to use some particular parameters to denote some new Hilbert-type inequalities and the reverses with the best constant factors. A class of Hilbert-type inequalities with the general measurable kernels is considered.

Affiliation:

Guangzhou, Guangdong, P. R. China