Fractional Sobolev inequalities : symmetrization, isoperimetry and interpolation / Joaquim Martin, Mario Milman
Type de document : MonographieCollection : Astérisque, 366Langue : anglais.Pays: France.Éditeur : Paris : Société Mathématique de France, 2014Description : 1 vol. (127 p.) ; 24 cmISBN: 9782856297964.ISSN: 0303-1179.Bibliographie : Bibliogr. p.[121]-127.Sujet MSC : 46-02, Research exposition (monographs, survey articles) pertaining to functional analysis46E35, Functional analysis - Linear function spaces and their duals, Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems
26D10, Real functions - Inequalities in real analysis, Inequalities involving derivatives and differential and integral operators
26A33, Real functions - Functions of one variable, Fractional derivatives and integralsEn-ligne : Résumé
| Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie
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CMI Salle 1 | Séries SMF 366 (Browse shelf(Opens below)) | Available | 12353-01 |
Bibliogr. p.[121]-127
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 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. (SMF)
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