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Fractional Sobolev inequalities :sym...

Martín, Joaquim.

Fractional Sobolev inequalities :symmetrization, isoperimetry and interpolation /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Fractional Sobolev inequalities :Joaquim Martín, Mario Milman.
其他題名:	symmetrization, isoperimetry and interpolation /
作者:	Martín, Joaquim.
其他作者:	Milman, Mario.
出版者:	Paris :Société mathématique de France publié avec le concours du Centre National de la Recherche Scientifique,2014.
面頁冊數:	viii, 127 p. ;24 cm.
標題:	Inequalities (Mathematics)
ISBN:	285629796X (pbk.)

Fractional Sobolev inequalities :symmetrization, isoperimetry and interpolation /
Martín, Joaquim.

Fractional Sobolev inequalities :symmetrization, isoperimetry and interpolation /Joaquim Martín, Mario Milman. - Paris :Société mathématique de France publié avec le concours du Centre National de la Recherche Scientifique,2014. - viii, 127 p. ;24 cm. - Astérisque,3660303-1179 ;.

Includes bibliographical references (p. [121]-127).

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.

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

In English; abstract also in French.

ISBN: 285629796X (pbk.)

LCCN: 2015382880Subjects--Topical Terms:

183909
Inequalities (Mathematics)

LC Class. No.: QA611.28 / .M381 2014

Fractional Sobolev inequalities :symmetrization, isoperimetry and interpolation /
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100 1 $a Martín, Joaquim. $3 796210
245 1 0 $a Fractional Sobolev inequalities : $b symmetrization, isoperimetry and interpolation / $c Joaquim Martín, Mario Milman.
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300 $a viii, 127 p. ; $c 24 cm.
490 0 $a Astérisque, $x 0303-1179 ; $v 366
504 $a Includes bibliographical references (p. [121]-127).
505 0 # $a 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.
520 # $a 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
546 $a In English; abstract also in French.
650 # 0 $a Inequalities (Mathematics) $3 183909
650 # 0 $a Metric spaces. $3 186150
650 # 0 $a Sobolev spaces. $3 247270
700 1 # $a Milman, Mario. $3 648241
710 2 # $a Société mathématique de France. $3 796211