Fractional Sobolev inequalities
Subtitle: symmetrization, isoperimetry and interpolation
By: Joaquim Martín, Mario Milman
Contributors: Milman, Mario, author; Société mathématique de France
Series: Astérisque -- 366
Publisher: Société mathématique de France publié avec le concours du Centre National de la Recherche Scientifique
Published: 2014
Place of publication: Paris
Language: eng
Number of pages: 127
ISBN-13: 9782856297964
Copyright date: 2014
Subjects: Metric spaces; Inequalities (Mathematics); Sobolev spaces
Description: 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
Notes: Includes bibliographical references (pages 121-127).

In English; abstract also in French.
Table of contents: title: Introduction; title: Preliminaries; title: Oscillations, K-functionals and isoperimetry; title: Embedding into continuous functions; title: Examples of applications; title: Fractional Sobolev inequaliteis in Gaussian measures; title: On limiting Sobolev embeddings and BMO; title: Estimation of growth "envelopes"; title: Lorentz spaces with negative indices; title: Connection with the work of Garsia and his collaborators; title: Some remarks on the calculation of K-functionals.