Fractional Sobolev inequalities symmetrization, isoperimetry and interpolation Joaquim Martín; Mario Milman

Zs.fassung in engl. und frz. Sprache

IntroductionPreliminaries -- Oscillations, K-functionals and isoperimetry -- Embedding into continuous functions -- Examples of applications -- Fractional Sobolev inequaliteis in Gaussian measures -- On limiting Sobolev embeddings and BMO -- Estimation of growth "envelopes" -- Lorentz spaces with negative indices -- Connection with the work of Garsia and his collaborators -- Some remarks on the calculation of K-functionals.

We obtain new oscillation inequalities in metric spaces in terms of the Peetre K-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 Polya-Szego principle that allows us to obtain continuity as a self improvement from boundedness, using symmetrization inequalities. Our methods also allow for preices 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.-Provided by publisher

Martín, Joaquim: Fractional Sobolev inequalities