scholarly journals Poincaré Inequalities for Mutually Singular Measures

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Andrea Schioppa
Keyword(s):  
Metric Space ◽  
Inverse System ◽  
Metric Graphs ◽  
Poincaré Inequalities ◽  
Singular Measures ◽  
Poincare Inequalities

Abstract Using an inverse system of metric graphs as in [3], we provide a simple example of a metric space X that admits Poincaré inequalities for a continuum of mutually singular measures.

scholarly journals COARSE EMBEDDINGS INTO A HILBERT SPACE, HAAGERUP PROPERTY AND POINCARÉ INEQUALITIES

2009 ◽  
Vol 01 (01) ◽  
pp. 87-100 ◽  
Author(s):  
ROMAIN TESSERA
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Metric Space ◽  
Unitary Representations ◽  
Poincaré Inequalities ◽  
Haagerup Property ◽  
Relative Property ◽  
Poincare Inequalities ◽  
Isometric Actions ◽  
Property T

We prove that a metric space does not coarsely embed into a Hilbert space if and only if it satisfies a sequence of Poincaré inequalities, which can be formulated in terms of (generalized) expanders. We also give quantitative statements, relative to the compression. In the equivariant context, our result says that a group does not have the Haagerup Property if and only if it has relative property T with respect to a family of probabilities whose supports go to infinity. We give versions of this result both in terms of unitary representations, and in terms of affine isometric actions on Hilbert spaces.

Poincaré inequalities for linearizations of very fast diffusion equations

Nonlinearity ◽  
2002 ◽  
Vol 15 (3) ◽  
pp. 565-580 ◽  
Author(s):  
J A Carrillo ◽  
C Lederman ◽  
P A Markowich ◽  
G Toscani
Keyword(s):  
Diffusion Equations ◽  
Fast Diffusion ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Fast Diffusion Equations

scholarly journals ORLICZ–POINCARÉ INEQUALITIES

2008 ◽  
Vol 51 (2) ◽  
pp. 529-543 ◽  
Author(s):  
Feng-Yu Wang
Keyword(s):  
Porous Media ◽  
Probability Measure ◽  
Poincaré Inequality ◽  
Dirichlet Forms ◽  
Sobolev Inequalities ◽  
Young Function ◽  
Poincare Inequality ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Porous Media Equations

AbstractCorresponding to known results on Orlicz–Sobolev inequalities which are stronger than the Poincaré inequality, this paper studies the weaker Orlicz–Poincaré inequality. More precisely, for any Young function $\varPhi$ whose growth is slower than quadric, the Orlicz–Poincaré inequality$$ \|f\|_\varPhi^2\le C\E(f,f),\qquad\mu(f):=\int f\,\mathrm{d}\mu=0 $$is studied by using the well-developed weak Poincaré inequalities, where $\E$ is a conservative Dirichlet form on $L^2(\mu)$ for some probability measure $\mu$. In particular, criteria and concrete sharp examples of this inequality are presented for $\varPhi(r)=r^p$ $(p\in[1,2))$ and $\varPhi(r)= r^2\log^{-\delta}(\mathrm{e} +r^2)$ $(\delta>0)$. Concentration of measures and analogous results for non-conservative Dirichlet forms are also obtained. As an application, the convergence rate of porous media equations is described.

scholarly journals Geometric characterizations of $p$-Poincaré inequalities in the metric setting

2016 ◽  
Vol 60 ◽  
pp. 81-111 ◽  
Author(s):  
E. Durand-Cartagena ◽  
J. A. Jaramillo ◽  
N. Shanmugalingam
Keyword(s):  
Poincaré Inequalities ◽  
Poincare Inequalities
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