The Equivalent Conditions of the Optimal Hilbert-Type Multiple Series Inequality with Quasi-Homogeneous Kernel

On a Hardy-Hilbert-Type Inequality with a General Homogeneous Kernel

By the method of weight coefficients and techniques of real analysis, a Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. The equivalent forms, the operator expressions with the norm, the reverses and some particular examples are also considered.

An extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel

In this paper, by the use of the weight coefficients, the transfer formula and the technique of real analysis, an extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions and a few examples are considered.

A Hilbert-Type Integral Inequality in the Whole Plane with the Homogeneous Kernel of Degree -2

on a hardy-hilbert-type inequality with a general homogeneous kernel

by the method of weight coefficients and techniques of real analysis, ahardy-hilbert-type inequality with a general homogeneous kernel and a bestpossible constant factor is given. the equivalent forms, the operatorexpressions with the norm, the reverses and some particular examples are alsoconsidered.

The necessary and sufficient conditions for the existence of a kind of Hilbert-type multiple integral inequality with the non-homogeneous kernel and its applications

*Correspondence: [email protected] 2Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P.R. China Full list of author information is available at the end of the article Abstract For x = (x1, . . . , xn), u(x) = ( ∑n i=1 aix ρ i ) 1/ρ , v(y) = ( ∑n i=1 biy ρ i ) 1/ρ , by using the methods and techniques of real analysis, the sufficient and necessary conditi...