we derive whole series of new integral inequalities of the hardy-type, with non-conjugate exponents. first, we prove and discuss two equivalent general inequa-li-ties 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. ...

We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties 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. ...

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 paper studies the weighted weak type inequalities for the Hardy operator as an operator from weighted L to weighted weak L in the case p = 1. It considers two different versions of the Hardy operator and characterizes their weighted weak type inequalities when p = 1. It proves that for the classical Hardy operator, the weak type inequality is generally weaker when q < p = 1. The best consta...

* Correspondence: [email protected] Department of Engineering Sciences and Mathematics, LuleåUniversity of Technology SE 971 87 Luleå, Sweden Full list of author information is available at the end of the article Abstract First we present and discuss an important proof of Hardy’s inequality via Jensen’s inequality which Hardy and his collaborators did not discover during the 10 years of research ...

In this paper, we prove a variant of a general Hardy-Knopp type inequality. We also formulate a convolution inequality in the language of topological groups. By our main results we obtain a general form of multidimensional strengthened Hardy and Pólya-Knopp-type inequalities.

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the rever...