Related papers: A new multicomponent Poincar\'e-Beckner inequality
A sharp Poincar\'e-type inequality is derived for the restriction of the Gaussian measure on the boundary of a convex set. In particular, it implies a Gaussian mean-curvature inequality and a Gaussian iso second-variation inequality. The…
In this paper we present a new approach to proving some exponential inequalities involving the sinc function. Power series expansions are used to generate new polynomial inequalities that are sufficient to prove the given exponential…
We show that certain functional inequalities, e.g.\ Nash-type and Poincar\'e-type inequalities, for infinitesimal generators of $C_0$ semigroups are preserved under subordination in the sense of Bochner. Our result improves \cite[Theorem…
Using some harmonic extensions on the upper-half plane, and probabilistic representations, and curvature-dimension inequalities with some negative dimensions, we obtain some new opimal functional inequalities of the Beckner type for the…
In this paper we study several inequalities of log-Sobolev type for Dunkl operators. After proving an equivalent of the classical inequality for the usual Dunkl measure $\mu_k$, we also study a number of inequalities for probability…
We introduce a new operation between nonnegative integrable functions on $\mathbb{R} ^n$, that we call geometric combination; it is obtained via a mass transportation approach, playing with inverse distribution functions. The main feature…
We introduce notions of dynamic gradient flows on time-dependent metric spaces as well as on time-dependent Hilbert spaces. We prove existence of solutions for a class of time dependent energy functionals in both settings. In particular we…
We establish a general scale-dependent Poincar\'{e}-Hardy type identity involving a vector field on the hyperbolic space. By choosing suitable parameter, potential and vector field in this identity, we can recover, as well as derive new…
We establish a quantitative isoperimetric inequality for weighted Riemannian manifolds with $\mathrm{Ric}_{\infty} \ge 1$. Precisely, we give an upper bound of the volume of the symmetric difference between a Borel set and a sub-level (or…
We prove an intrinsic equivalence between strong hypercontractivity and a strong logarithmic Sobolev inequality for the cone of logarithmically subharmonic functions. We introduce a new large class of measures, Euclidean regular and…
We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topological characterization of indecomposability which is new even in…
We investigate properties of measures in infinite dimensional spaces in terms of Poincar\'e inequalities. A Poincar\'e inequality states that the $L^2$ variance of an admissible function is controlled by the homogeneous $H^1$ norm. In the…
In this paper, we prove a couple of new nonlinear functional inequalities of Sobolev type akin to the logarithmic Sobolev inequality. In particular, one of the inequalities reads $$ \int_{\mathbb{S}^1}\arctan\left(\frac{\partial_x…
The goal of this paper is to continue the study of the relation between the Poincar\'e inequality and the lower bounds of Minkowski content of separating sets, initiated in our previous work [Caputo, Cavallucci: Poincar\'e inequality and…
The paper is concerned with the change of probability measures $\mu$ along non-random probability measure valued trajectories $\nu_t$, $t\in [-1,1]$. Typically solutions to non-linear PDEs, modeling spatial development as time progresses,…
We consider Gagliardo-Nirenberg inequalities on the sphere which interpolate between the Poincar\'e inequality and the Sobolev inequality, and include the logarithmic Sobolev inequality as a special case. We establish explicit stability…
In this paper we will establish different weighted Poincar\'{e} inequalities with variable exponents on Carnot-Carath\'{e}odory spaces or Carnot groups. We will use different techniques to obtain these inequalities. For vector fields…
We consider Markov random fields of discrete spins on the lattice $\Zd$. We use a technique of coupling of conditional distributions. If under the coupling the disagreement cluster is "sufficiently" subcritical, then we prove the Poincar\'e…
For a class of potentials $\psi$ satisfying a condition depending on the roof function of a suspension (semi)flow, we show an EKP inequality, which can be interpreted as a H\"older continuity property in the weak${^*}$ norm of measures,…
The main aim of this note is to prove a sharp Poincar\'e-type inequality for vector-valued functions on $\mathbb{S}^2$, that naturally emerges in the context of micromagnetics of spherical thin films.