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].…”

An equivalent property of a Hilbert-type integral inequality and its applications

“…In 2013, Yang [25] also studied the equivalence of ( 6) and (7) by adding a condition h(u) = k λ (u, 1). In 2017, Hong [9] studied an equivalent condition for (6) involving certain parameters, and some further related results were established in [4], [5], [15], [29], [28].…”