Fractional Sobolev inequalities: Symmetrization, isoperimetry and interpolation

Joaquim Martín, Mario Milman

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

We obtain new oscillation inequalities in metric spaces in terms of the Peetre if-functional and the isoperimetric profile. Applications provided include a detailed study of Fractional Sobolev inequalities and the Morrey-Sobolev embedding theorems in different contexts. In particular we include a detailed study of Gaussian measures as well as probability measures between Gaussian and exponential. We show a kind of reverse Pólya-Szegö principle that allows us to obtain continuity as a self improvement from boundedness, using symmetrization inequalities. Our methods also allow for precise estimates of growth envelopes of generalized Sobolev and Besov spaces on metric spaces. We also consider embeddings into BMO and their connection to Sobolev embeddings.
Original languageEnglish
Pages (from-to)1-136
JournalAsterisque
Issue number366
Publication statusPublished - 1 Jan 2015

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