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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Hilbert-Type Inequalities with the Homogeneous Kernel of Degree -1

Pp. 27-53 (27)

Bicheng Yang

Abstract

In this chapter, by using the way of weight coefficients and the technique of real analysis, some basic theorems and corollaries on the discrete Hilbert-type inequalities with the homogeneous kernel of degree -1 are given. We apply some relating results mentioned in Chap ter 2 to building some Hilbert-type in equalities with a particular homogeneous kernel of degree -1. The strengthened vers ions, the reverses and the more accurate Hilbert-type inequalities are considered. The proofs about the best possible property of the constant factors are left in Chapter 4. In some particular examples of this chapter, the improved Euler-Maclaurin summation formulas mentioned in Charter 2 and are used here.

Affiliation:

Guangzhou, Guangdong, P. R. China