Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel

Abstract

Let Gu,v be a homogeneous nonnegative function of order λ,Kn,xm,ρ=Gnλ1,xm,ρλ2. By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple integral inequality ∫ℝ+m ∑n=1∞ Kn,xm,ρanfxdx≤Ma~p,αfq,β are discussed. Finally, its applications in operator theory are discussed.

Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities

“…In 2017, Hong [18] proved an equivalent condition between (3) and a few parameters. Some similar results were obtained in [19][20][21][22][23][24][25][26][27][28].…”

A New Hardy–Hilbert-Type Integral Inequality Involving One Multiple Upper Limit Function and One Derivative Function of Higher Order

“…In 2016-2017, Hong et al [17,18] presented several equivalent statements of the extensions of ( 1) and (2) with the best possible constant factors and multi-parameters. Some similar results were established in [19][20][21][22][23][24][25][26][27].…”

A New Reverse Extended Hardy–Hilbert’s Inequality with Two Partial Sums and Parameters

“…In 2016, by using the weight coefficients and the techniques of real analysis, Hong et al [18] considered a few equivalent statements of the generalization of (1) with the best possible constant factor related to multi-parameters. The other further results were obtained by [19][20][21][22][23][24][25][26][27][28][29].…”