Symmetrization Inequalities for Probability metric spaces with Convex Isoperimetric profile
Joaquim Martin, Walter A. Ortiz
TL;DR
This paper develops symmetrization inequalities for probability metric spaces with convex isoperimetric profiles, enabling a unified approach to sharp Sobolev-Poincaré and Nash inequalities.
Contribution
It introduces symmetrization inequalities that incorporate the isoperimetric estimator, unifying the treatment of key functional inequalities in probability metric spaces.
Findings
Established symmetrization inequalities for convex isoperimetric profiles.
Unified framework for sharp Sobolev-Poincaré and Nash inequalities.
Potential applications in analysis on probability metric spaces.
Abstract
We obtain symmetrization inequalities on probability metric spaces with convex isoperimetric profile which incorporate in their formulation the isoperimetric estimator and that can be applied to provide a unified treatment of sharp Sobolev-Poincar\'{e} and Nash inequalities.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Point processes and geometric inequalities · Geometric Analysis and Curvature Flows