Discrete Hilbert-Type Inequalities

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

Author(s): Bicheng Yang

Pp: 27-53 (27)

Doi: 10.2174/978160805242411101010027

* (Excluding Mailing and Handling)

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.

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