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, 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.

The aim of this paper is to study Sobolev-type embeddings and their optimality. We work in the frame of rearrangement-invariant norms and unbounded domains. We establish the equivalence of a Sobolev embedding to the boundedness of a certain Hardy operator on some cone of positive functions. This Hardy operator is then used to provide optimal domain and range rearrangement-invariant norm in the ...

In this paper, we present a version of horizontal weighted Hardy–Rellich type and Caffarelli–Kohn– Nirenberg type inequalities on stratified groups and study some of their consequences. Our results reflect on many results previously known in special cases. Moreover, a new simple proof of the Badiale–Tarantello conjecture [2] on the best constant of a Hardy type inequality is provided. We also s...

We characterize the good weights for a certain weighted weak-type iterated Hardy inequality to hold. As consequence, we get characterizations of some bilinear inequalities.

for every u∈W1,p(Rn). It is easy to see that the proposition fails when s > 1, where s = q/p. In this paper we are trying to find out what happens if s > 1. We show that it does not only become true but obtains better estimates. The described result is stated and proved in Section 3. The method invoked is different from that by Cazenave in [2]; it relies on some Littlewood-Paley theory and Beso...

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...

In the present article, we prove some new generalizations of dynamic inequalities Hardy-type by utilizing diamond-? integrals on time scales. Furthermore, in two variables scales are proved. Moreover, Hardy for several functions using The results proved Jensen inequality and Fubini theorem Our main extend existing integral discrete inequalities. Symmetry plays an essential role determining corr...