We prove a Hardy-Littlewood type inequality with respect to a system called Vilenkin-like system (which is a common generalisation of several well-known systems ) in the two-dimensional case.

We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces on half-spaces. Our proof relies on a non-linear and non-local version of the ground state representation.

Abstract The aim of this work is to obtain quantum estimates for q -Hardy type integral inequalities on calculus. For this, we establish new identities including derivatives and numbers. After that, prove a generalized -Minkowski inequality. Finally, with the help obtained equalities inequality, results want. outcomes presented in paper are -extensions -generalizations comparable literature ine...

We show that the Hardy-Littlewood maximal operator and a class of Calderón-Zygmund singular integrals satisfy the strong type modular inequality in variable L spaces if and only if the variable exponent p(x) ∼ const.

In this paper necessary and sufficient conditions for the validity of the generalized Hardy inequality for the case −∞ < q p < 0 and 0 < p q < 1 are derived. Furthermore, some special cases are considered.

In this paper, we derive an anisotropic Picone identity for the anisotropic Laplacian, which contains some known Picone identities. As applications, a Sturmian comparison principle to the anisotropic elliptic equation and an anisotropic Hardy type inequality are shown.

We show that the Hardy-Littlewood maximal operator and a class of CalderónZygmund singular integrals satisfy the strong type modular inequality in variable Lp spaces if and only if the variable exponent p(x) ∼ const.

Some new criteria for the oscillation of certain difference equations with mixed nonlinearities are established. The main tool in the proofs is an inequality due to Hardy, Littlewood, and Pólya. c © 2006 Elsevier Ltd. All rights reserved.