For probability metric spaces with a convex isoperimetric estimator, the paper establishes a pointwise rearrangement inequality and uses it to derive unified Sobolev-Poincaré and Nash inequalities.
Levels of concentration between exponential and Gaussian, Ann
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Symmetrization Inequalities for Probability metric spaces with Convex Isoperimetric profile
For probability metric spaces with a convex isoperimetric estimator, the paper establishes a pointwise rearrangement inequality and uses it to derive unified Sobolev-Poincaré and Nash inequalities.