Related papers: On Hardy-Sobolev embedding

We present new estimate for Hardy-type inequality in variable exponent Lebesgue spaces. More precisely, by imposing regularity assumptions on the exponent, we prove that the estimations can be reduced to the fixed exponents.

We present a simple proof of some interpolation inequalities between H\"{o}lder and Lebesgue's spaces. As an example, to demonstrate the simplicity of their applications to nonlinear PDE, we give also a simple proof of an a-priory estimate…

We present a unified strategy to derive Hardy-Poincar\'e inequalities on bounded and unbounded domains. The approach allows proving a general Hardy-Poincar\'e inequality from which the classical Poincar\'e and Hardy inequalities immediately…

In this paper we obtain the sharp estimates for the mixed $\left( \ell_{1},\ell _{2}\right) $-Littlewood inequality for real scalars with exponents $\left(2,1,2,2....,2\right) .$ These results are applied to find sharp estimates for the…

In this work, we have proved a version of the Hardy-Littlewood-Sobolev inequality for variable exponents. After we use the variational method to establish the existence of solution for a class of Choquard equations involving the…

Multilinear embedding estimates for the fractional Laplacian are obtained in terms of functionals defined over a hyperbolic surface. Convolution estimates used in the proof enlarge the classical framework of the convolution algebra for…

This paper is mainly devoted to the study of the reversed Hardy-Littlewood-Sobolev (HLS) inequality on Heisenberg group $\mathbb{H}^n$ and CR sphere $\mathbb{S}^{2n+1}$. First, we establish the roughly reversed HLS inequality and give a…

We investigate the growth of the constants of the polynomial Hardy-Littlewood inequality.

We use different approaches to study a generalization of a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality. Our results lead naturally to the study of weighted remainder form of Hardy-type…

We prove non local Hardy inequalities on Carnot groups and Riemannian manifolds, relying on integral representations of fractional Sobolev norms.

We prove non local Hardy inequalities on Carnot groups and Riemannian manifolds, relying on integral representations of fractional Sobolev norms.

In this paper, we study the stability of the following nonlocal Soblev-type inequality \begin{equation*} C_{HLS}\big(\int_{\mathbb{R}^n}\big(|x|^{-\mu} \ast u^{p}\big)u^{p} dx\big)^{\frac{1}{p}}\leq\int_{\mathbb{R}^n}|\nabla u|^2 dx , \quad…

We show that interpolation results in the $S$-nodes theory may be considered as Khrushchev-type formulas. If separation of the well-known Verblunsky (Schur) coefficients occurs in Khrushchev formulas, the separation of the so the called new…

In this paper we extend Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds for dimension $n\ne 2$. As one application, we solve a generalized Yamabe problem on locally conforamlly flat manifolds via a new designed energy…

We formulate and prove a generalization of Hardy's inequality (Hardy,1925) in terms of random variables and show that it contains the usual (or familiar) continuous and discrete forms of Hardy's inequality. Next we improve the recent…

Given a metric measure space $X$, we consider a scale of function spaces $T^{p,q}_s(X)$, called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on…

In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional…

In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy--Littlewood constants for $2$-homogeneous polynomials on $\ell_p^2$ spaces, $2<p\leq\infty$…

The main purpose of this article is to obtain (weighted) fractional Hardy inequalities with a remainder and fractional Hardy-Sobolev-Maz'ya inequalities valid for $1<p<2$.

We develop a unified H\"older Lebesgue scale \(X^p\) and its weighted, higher order variants \(X^{k,p,a}\) to extend the Caffarelli Kohn Nirenberg (CKN) inequality beyond the classical Lebesgue regime. Within this framework we prove a two…