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. ...

in this paper, we reconstruct the hardy-littlewood’s inequality byusing the method of the weight coefficient and the technic of real analysis includinga best constant factor. an open problem is raised.

In the euclidean space, Sobolev and Hardy-Littlewood-Sobolev inequalities can be related by duality. In this paper, we investigate how to relate these inequalities using the flow of a fast diffusion equation in dimension d ≥ 3. The main consequence is an improvement of Sobolev’s inequality when d ≥ 5, which involves the various terms of the dual Hardy-Littlewood-Sobolev inequality. In dimension...

let and be a sequence with non-negative entries. if , denote by the infimum of those satisfying the following inequality: whenever . the purpose of this paper is to give an upper bound for the norm of operator t on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). we considered this problem for certain matrix operators such as norlund, weighted mean, ceasaro and copson matrices. th...

1.1. Hardy-Sobolev-Maz’ya inequalities. Hardy inequalities and Sobolev inequalities bound the size of a function, measured by a (possibly weighted) L norm, in terms of its smoothness, measured by an integral of its gradient. Maz’ya [22] proved that for functions on the half-space R+ = {x ∈ R : xN > 0}, N ≥ 3, which vanish on the boundary, the sharp version of the Hardy inequality can be combine...

* 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 reconstruct the Hardy-Littlewood’s inequality byusing the method of the weight coefficient and the technic of real analysis includinga best constant factor. An open problem is raised.

Differential forms are interesting and important generalizations of real functions and distributions. Many interesting results and applications of differential forms have recently been found in some fields. As an important tool the Hardy-Littlewood inequality have been playing critical roles in many mathematics, including potential analysis, partial differential equations and the theory of elas...

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...

The Hardy inequality ∫ Ω |u(x)|pd(x)−p dx c ∫ Ω |∇u(x)|p dx with d(x) = dist(x, ∂Ω) holds for u ∈ C∞ 0 (Ω) if Ω ⊂ n is an open set with a sufficiently smooth boundary and if 1 < p < ∞. P.Haj lasz proved the pointwise counterpart to this inequality involving a maximal function of Hardy-Littlewood type on the right hand side and, as a consequence, obtained the integral Hardy inequality. We extend...