Related papers: Logarithmic Sobolev inequality revisited

We give estimates on the logarithmic Sobolev constant of some finite lamplighter graphs in terms of the spectral gap of the underlying base. Also, we give examples of application.

We obtain an improved Sobolev inequality in H^s spaces involving Morrey norms. This refinement yields a direct proof of the existence of optimizers and the compactness up to symmetry of optimizing sequences for the usual Sobolev embedding.…

We derive sufficient conditions for a probability measure on a finite product space (a spin system) to satisfy a (modified) logarithmic Sobolev inequality. We establish these conditions for various examples, such as the (vertex-weighted)…

We relate transport-entropy inequalities to the study of critical points of functionals defined on the space of probability measures. This approach leads in particular to a new proof of a result by Otto and Villani [43] showing that the…

The Riesz-Sobolev inequality provides an upper bound, in integral form, for the convolution of indicator functions of subsets of Euclidean space. We formulate and prove a sharper form of the inequality. This can be equivalently phrased as a…

In this paper we present a new characterization of Sobolev spaces on Euclidian spaces ($\mathbb{R}^n$). Our characterizing condition is obtained via a quadratic multiscale expression which exploits the particular symmetry properties of…

We will prove a reverse Rogers-Shephard inequality for log-concave functions. In some particular cases, the method used for general log-concave functions can be slightly improved, allowing us to prove volume estimates for polars of…

We reconstruct a function by values of its Segal-Bargmann transform at points of a lattice.

In this paper we explore a new method of analysis of associative algebras.

In this paper we establish a new class of weighted Hardy-Sobolev type inequalities under mild monotonicity assumptions on the weight function. As a consequence, we derive the corresponding weighted Sobolev and trace-type inequalities. These…

The purpose of this paper is twofold. We first prove a weighted Sobolev inequality and part of a weighted Morrey's inequality, where the weights are a power of the mean curvature of the level sets of the function appearing in the…

We prove several Sobolev inequalities, which are then used to establish a fractional Hardy-Sobolev- Maz'ya inequality on the upper halfspace.

We show that even mild improvements of the Polya-Vinogradov inequality would imply significant improvements of Burgess' bound on character sums. Our main ingredients are a lower bound on certain types of character sums (coming from works of…

We establish a fourth order sharp Sobolev trace inequality on three-balls, and its equivalence to a third order sharp Sobolev inequality on two-spheres.

In this survey, we review the many faces of the Hornich-Hlawka inequality. Several open problems that seem of utmost interest are mentioned.

On the framework of the 2-adic group Z_2, we study a Sobolev-like inequality where we estimate the L^2 norm by a geometric mean of the BV norm and the Besov space B(-1,\infty,\infty) norm. We first show, using the special topological…

This paper provides a new regularization method which is particularly suitable for linear exponentially ill-posed problems. Under logarithmic source conditions (which have a natural interpretation in terms of Sobolev spaces in the…

We study the log-concave measures, their characterization via the Pr\'ekopa-Leindler property and also define a subset of it whose elements are called super log-concave measures which have the property of satisfying a logarithmic Sobolev…

This is a short overview of some recent tendencies in the theory of linear inequalities that are evoked by Boolean valued analysis.

In this paper, the new weighted inequalities were derived by-distance which is similar to the given inequality for the potential operator defined in [1].