Related papers: Chord Sobolev inequalities

We obtain sharp fractional Hardy inequalities for the half-space and for convex domains. We extend the results of Bogdan and Dyda and of Loss and Sloane to the setting of Sobolev-Bregman forms.

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincar\'e inequality (for instance logarithmic Sobolev or $F$-Sobolev). The case of Poincar\'e and weak Poincar\'e inequalities was studied in…

We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse square weight, is controlled by the energy.…

We establish a sharp affine $L^p$ Sobolev trace inequality by using the $L_p$ Busemann-Petty centroid inequality. For $p = 2$, our affine version is stronger than the famous sharp $L^2$ Sobolev trace inequality proved independently by…

We prove fractional Sobolev-Poincar\'e inequalities, capacitary versions of fractional Poincar\'e inequalities, and pointwise and localized fractional Hardy inequalities in a metric space equipped with a doubling measure. Our results…

Motivated by the recent characterization of Sobolev spaces due to Brezis-Van Schaftingen-Yung we prove new weak-type inequalities for one parameter families of operators connected with mixed norm inequalities. The novelty here comes from…

We consider generalised Mehler semigroups and, assuming the existence of an associated invariant measure $\sigma$, we prove functional integral inequalities with respect to $\sigma$, such as logarithmic Sobolev and Poincar\'{e} type.…

The existence of extremal functions for the Sobolev trace inequalities is studied using the concentration compactness theorem. The conjectured extremal, the function of conformal factor, is considered and is proved to be an actual extremal…

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 review recent results on functional inequalities for systems of orthonormal functions. The key finding is that for various operators the orthonormality leads to a gain over a simple application of the triangle inequality. The operators…

In this article, we prove the existence of extremal functions in higher-order affine Sobolev inequalities. Proofs rely on concentration-compactness methods in spaces of integer or fractional regularity. The tools we use, available in spaces…

We give some estimates of the remainder terms for several conformally-invariant Sobolev-type inequalities on the Heisenberg group, in analogy with the Euclidean case. By considering the variation of associated functionals, we give a…

Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Lata{\l}a we provide a concentration inequality for non-necessarily Lipschitz functions $f\colon \R^n \to \R$ with bounded…

We establish the existence and uniqueness of limits at infinity along infinite curves outside a zero modulus family for functions in a homogeneous Sobolev space under the assumption that the underlying space is equipped with a doubling…

We establish a sharp Adams-type inequality invoking a Hardy inequality for any even dimension. This leads to a non compact Sobolev embedding in some Orlicz space. We also give a description of the lack of compactness of this embedding in…

We establishe an affine Hardy-Littlewood-Sobolev inequality concerning two different functions which is stronger than the classical Hardy-Littlewood-Sobolev inequality. Furthermore, we also prove reverse inequalities for the new…

This article investigates the Bohr phenomenon and sharp coefficient problems for the class $\mathcal{A}_{\beta}$, a subclass of analytic self-maps of the unit disk with the holomorphic generators of one-parameter continuous semigroups. By…

Threshold phenomena are investigated using a general approach, following Talagrand [Ann. Probab. 22 (1994) 1576--1587] and Friedgut and Kalai [Proc. Amer. Math. Soc. 12 (1999) 1017--1054]. The general upper bound for the threshold width of…

A comprehensive approach to Sobolev-type embeddings, involving arbitrary rearrangement- invariant norms on the entire Euclidean space R^n, is offered. In particular, the optimal target space in any such embedding is exhibited. Crucial in…

The present paper is devoted to analysis of the lack of compactness of bounded sequences in \emph{inhomogeneous} Sobolev spaces, where bounded sequences might fail to be compact due to an isometric group action, that is, \emph{translation}.…