We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequalities of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. In parti...

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.

Abstract By the use of weight coefficients and techniques real analysis, we establish a new Hardy–Mulholland-type inequality with mixed kernel best possible constant factor in terms hypergeometric function. Equivalent forms, an operator expression norm reverses are also considered.

By means of real analysis and weight functions, we obtain a few equivalent conditions of two kinds of Hardy-type integral inequalities with the non-homogeneous kernel and parameters. The constant factors related to the gamma function are proved to be the best possible. We also consider the operator expressions and some cases of homogeneous kernel.

The main objective of this paper is some new special Hilbert-type and HardyHilbert-type inequalities in (R) with k ≥ 2 non-conjugate parameters which are obtained by using the well known Selberg’s integral formula for fractional integrals in an appropriate form. In such a way we obtain extensions over the whole set of real numbers, of some earlier results, previously known from the literature, ...

Abstract. By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter where the constant factor is expressed in terms of the extended Riemann zeta function. Meanwhile, a few equivalent conditions for two kinds of Hardytype integral inequalities...

Abstract In this article, we first apply the method of combining interpolation theorem and weak-type estimate developed in Chen et al. to derive Hardy-Littlewood-Sobolev inequality with an extended Poisson kernel. By using weighted Hardy inequality, further obtain Stein-Weiss For extremal problem corresponding presence double-weighted exponents not being necessarily nonnegative makes it impossi...

We describe the large-time asymptotics of solutions to heat equation for fractional Laplacian with added subcritical or even critical Hardy-type potential. The is governed by a self-similar solution equation, obtained as normalized limit at origin kernel corresponding Feynman-Kac semigroup.

We consider a singular second order differential operator ∆ defined on ]0,∞[. We give nice estimates for the kernel which intervenes in the integral transform of the eigenfunction of ∆. Using these results, we establish Hardy type inequalities for Riemann-Liouville and Weyl transforms associated with the operator ∆.