A Half-Discrete Hilbert-Type Inequality with a Non-Homogeneous Kernel and Two Variables

Multidimensional Half-Discrete Hilbert-Type Inequalities and Operator Expressions

“…In this chapter, by the use of the methods of weight functions and technique of real analysis, two kinds of multidimensional more accurate half-discrete Hilbert-type inequalities with the best possible constant factors are given, which are extensions of (6) and Yang's [32] work. Equivalent forms and some reverses with the best constant factors are obtained.…”

“…At the same time, a halfdiscrete Hilbert-type inequality with a general nonhomogeneous kernel and a best constant factor is given by Yang [32] .…”

Reverse Hilbert inequalities involving series

“…The well-known Hilbert's inequality can be stated as below [6, p.226]. Hilbert's inequality and its integral form were studied extensively and numerous variants, generalizations, and extensions appeared in the literatures [2][3][4][5][7][8][9][10][11][12][13]16,17] and the references cited therein. Some researches on reverse Hilbert inequalities were published in [15,18,19] and et al In 1998, Pachpatte [14] proved some new inequalities similar to Hilbert's inequality (1.1).…”

A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function

“…Applying the weight functions, a half-discrete Hilbert-type inequality with a general homogeneous kernel of degree and a best constant factor is proved as follows ( cf. [ 29 ]): A half-discrete Hilbert-type inequality with a general non-homogeneous kernel and a best constant factor is given by Yang [ 30 ].…”