Related papers: Poincar\'e inequalities for mutually singular meas…

Let (N, G), where N is a normal subgroup of G<SL_n(C), be a pair of finite groups and V a finite-dimensional fundamental G-module. We study the G-invariants in the symmetric algebra S(V) by giving explicit formulas of the Poincar\'{e}…

A common approach to metric-affine, local Poincar\'e, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and…

This paper is devoted to Gaussian interpolation inequalities with endpoint cases corresponding to the Gaussian Poincar\'e and the logarithmic Sobolev inequalities, seen as limits in large dimensions of Gagliardo-Nirenberg-Sobolev…

Some related results to Pecaric's inequality in inner product spaces that generalises Bombieri's inequality, are given.

Let $(X,d)$ be a compact metric space. We consider the behavior of probability measures $\mu$ with the property that $$ \int_{X} d(x, y) d\mu(y) \qquad \mbox{is independent of}~x \in X.$$ It appears that such measures, when they exist,…

In this article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values…

Given $p \in (1,\infty)$, let $(\operatorname{X},\operatorname{d},\mu)$ be a metric measure space with uniformly locally doubling measure $\mu$ supporting a weak local $(1,p)$-Poincar\'e inequality. For each $\theta \in [0,p)$, we…

The following work demonstrates the viability of Poincar\'e symmetry in a discrete universe. We develop the technology of the discrete principal Poincar\'e bundle to describe the pairing of (1) a hypercubic lattice `base manifold' labeled…

Let $\MM$ be the space of finite measures on a Locally compact Polish space, and let $\BG$ be the Gamma distribution on $\MM$ with intensity measure $\nu\in \MM$. Let $\nn^{ext}$ be the extrinsic derivative with tangent bundle $T\MM=…

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincar\'{e} inequalities, general Beckner inequalities...). We also discuss the…

In this paper, we establish a condition on weighted graphs with finite measure that guarantees the validity of a global Poincar\'e inequality. This condition can be viewed as a discrete analogue of the criterion introduced by J. Boman in…

In this paper, the Harnack inequalities and super-Poincar\'{e} inequality for generalized CIR model are obtained. Since the noise is degenerate, the intrinsic metric has been introduced to construct the coupling by change of measure. By…

In this paper we give a geometric condition which ensures that $(q,p)$-Poincar\'e-Sobolev inequalities are implied from generalized $(1,1)$-Poincar\'e inequalities related to $L^1$ norms in the context of product spaces. The concept of…

We develop an analog to the ends of a metric space for the category of coarse metric spaces and show that it is equivalent to a previously defined coarse invariant.

Here we show existence of numerous subsets of Euclidean and metric spaces that, despite having empty interior, still support Poincar\'e inequalities. Most importantly, our methods do not depend on any rectilinear or self-similar structure…

In the setting of a metric space equipped with a doubling measure and supporting a Poincar\'e inequality, and based on results by Bj\"orn and Shanmugalingam (2007), we show that functions of bounded variation can be extended from any…

We complete the study of the regularity for Trudinger's equation by proving that weak solutions are H\"older continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a…

Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…

In this paper, we prove trace-type Poincar\'e and Sobolev inequalities for the space of functions of bounded $\mathbb{A}$-Variation

We initiate the study of fine $p$-(super)minimizers, associated with $p$-harmonic functions, on finely open sets in metric spaces, where $1 < p < \infty$. After having developed their basic theory, we obtain the $p$-fine continuity of the…