TY  - BOOK
AU  - Martín,Joaquim
AU  - Milman,Mario
TI  - Fractional Sobolev inequalities: symmetrization, isoperimetry and interpolation 
T2  - Asterisque
SN  - 9782856297964
U1  - 510=4 23
PY  - 2014///
CY  - Paris
PB  - Societe Mathematique de Franc
KW  - Metric spaces
KW  - Sobolev spaces
KW  - Inequalities (Mathematics)
N1  - Includes bibliographical references (pages 121-127); 1. Introduction -- 
2. Preliminaries -- 
3. Oscillations, K-functionals and isoperimetry -- 
4. Embedding into continuous functions -- 
5. Examples of applications -- 
6. Fractional Sobolev inequaliteis in Gaussian measures -- 
7. On limiting Sobolev embeddings and BMO -- 
8. Estimation of growth "envelopes" -- 
9. Lorentz spaces with negative indices -- 
10. Connection with the work of Garsia and his collaborators -- A. Some remarks on the calculation of K-functionals--
Bibliography
N2  - 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
ER  -