相关论文: Sharp Weight Hardy-Sobolev inequalities for Grand …

There are at least two directions concerning the extension of classical sharp Hardy-Littlewood-Sobolev inequality: (1) Extending the sharp inequality on general manifolds; (2) Extending it for the negative exponent $\lambda=n-\alpha$ (that…

In this short article we show a particular version of the Hedberg inequality which can be used to derive, in a very simple manner, functional inequalities involving Sobolev and Besov spaces in the general setting of Lebesgue spaces of…

In this paper the complete solution of the restricted inequalities for supremal operators are given. The boundedness of the composition of supremal operators with the Hardy and Copson operators in weighted Lebesgue spaces are characterized.

We establish both sufficient and necessary conditions for the validity of the so-called Hardy-Sobolev inequalities on open sets of the Euclidean space. These inequalities form a natural interpolating scale between the (weighted) Sobolev…

Let $\Omega$ be an open set in a metric measure space $X$. Our main result gives an equivalence between the validity of a weighted Hardy-Sobolev inequality in $\Omega$ and quasiadditivity of a weighted capacity with respect to Whitney…

Upper and lower estimates are obtained for the Schatten-von Neumann norms of the Hardy-Steklov operator in Lebesgue function spaces on the semi-axis.

In this short article we obtain the non-asymptotic upper and low estimations for linear and bilinear weight Riesz's functional through the Lebesgue spaces.

We develop the notions of hypercontractivity (HC) and the log-Sobolev (LS) inequality for completely bounded norms of one-parameter semigroups of super-operators acting on matrix algebras. We prove the equivalence of the completely bounded…

This paper is devoted to Hardy type inequalities with remainders for compactly supported smooth functions on open sets in the Euclidean space. We establish new inequalities with weight functions depending on the distance function to the…

We study the sharp constant in the Hardy inequality for fractional Sobolev spaces defined on open subsets of the Euclidean space. We first list some properties of such a constant, as well as of the associated variational problem. We then…

We obtain a pointwise description of functions belonging to function spaces with the lattice property. In particular, it is valid for Banach function spaces provided that the Hardy-Littlewood maximal operator is bounded. We also study…

This paper is devoted to logarithmic Hardy-Littlewood-Sobolev inequalities in the two-dimensional Euclidean space, in presence of an external potential with logarithmic growth. The coupling with the potential introduces a new parameter,…

We extend the classical Lyapunov inequality on the measurable space with infinite measure and on the so-called Grand Lebesgue spaces (GLS). We find also the exact value for correspondent constant. Possible applications: Functional Analysis…

In this paper, we obtain the reversed Hardy-Littlewood-Sobolev inequality with vertical weights on the upper half space and discuss the extremal functions. We show that the sharp constants in this inequality are attained by introducing a…

We obtain sharp Hardy inequalities on antisymmetric functions where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the previously published paper \cite{HL}, where Hardy's inequalities were…

We deal with weighted Hardy-Sobolev type inequalities for functions on $\mathbb{R}^d$, $d\geq 2$. The weights involved are anisotropic, given by products of powers of the distance to the origin and to a nontrivial subspace. We establish…

In this article, we introduce and study capacities related to nonlocal Sobolev spaces, with focus on spaces corresponding to zero-order nonlocal operators. In particular, we prove Hardy-type inequalities to obtain Sobolev embeddings and use…

By using, among other things, the Fourier analysis techniques on hyperbolic and symmetric spaces, we establish the Hardy-Sobolev-Maz'ya inequalities for higher order derivatives on half spaces. The proof relies on a Hardy-Littlewood-Sobolev…

The aim of this paper is to provide Markov-type inequalities in the setting of weighted Sobolev spaces when the considered weights are generalized classical weights. Also, as results of independent interest, some basic facts about Sobolev…

In this article we compute the best Sobolev constants for various Hardy-Sobolev inequalities with sharp Hardy term. This is carried out in three different environments: interior point singularity in Euclidean space, interior point…