Fractional Poincaré inequalities for general measures (original) (raw)

Abstract

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This paper establishes fractional Poincaré inequalities for general measures on R^n, focusing on measures that can be expressed as M = e^{-V} for some sufficiently regular function V. It investigates the implications of nonlocal quantities and the conditions under which such inequalities hold, particularly under assumptions involving the behavior of the measure at infinity. The results contribute to the understanding of Sobolev spaces and the interplay between the measure and the Poincaré inequality.

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  21. Clément Mouhot-University of Cambridge, DAMTP Wilberforce road, Cambridge CB3 0WA, England On leave from: CNRS & École Normale Supérieure, DMA, 45, rue d'Ulm -F 75230 Paris cedex 05, France Emmanuel Russ-Université Aix-Marseille III, LATP, Faculté des Sciences et Techniques, Case cour A Avenue Escadrille Normandie-Niemen, F-13397 Marseille, Cedex 20, France et CNRS, LATP, CMI, 39 rueF. Joliot-Curie, F-13453 Marseille Cedex 13, France Yannick Sire-Université Aix-Marseille III, LATP, Faculté des Sciences et Techniques, Case cour A Avenue Escadrille Normandie-Niemen, F-13397 Marseille, Cedex 20, France et CNRS, LATP, CMI, 39 rueF. Joliot-Curie, F-13453 Marseille Cedex 13, France