Fractional Sobolev inequalities : symmetrization, isoperimetry and interpolation

Fractional Sobolev inequalities : symmetrization, isoperimetry and interpolation /

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 det...

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Bibliographic Details
Main Authors: Martín, Joaquim (Author), Milman, Mario (Author)
Format: Book
Language:English
Published: Paris : Société mathématique de France, 2014.
Series:Astérisque 366.
Subjects:
Metric spaces.
Sobolev spaces.
Inequalities (Mathematics)
Metric spaces
Sobolev spaces
Table of Contents:
  • Introduction
  • Preliminaries
  • 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.

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