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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Symmetrization inequalities and Sobolev embeddings

Authors: Joaquim Martín and Mario Milman
Journal: Proc. Amer. Math. Soc. 134 (2006), 2335-2347
MSC (2000): Primary 46E30, 26D10
Published electronically: February 6, 2006
MathSciNet review: 2213707
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Abstract: We prove new extended forms of the Pólya-Szegö symmetrization principle. As a consequence new sharp embedding theorems for generalized Besov spaces are proved, including a sharpening of the limiting cases of the classical Sobolev embedding theorem. In particular, a surprising self-improving property of certain Sobolev embeddings is uncovered.

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Additional Information

Joaquim Martín
Affiliation: Department de Matemàtiques, Universitat Autónoma de Barcelona, 08193 Bellaterra (Barcelona) Spain

Mario Milman
Affiliation: Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431

Keywords: Symmetrization, Besov spaces, Sobolev spaces, rearrangement invariant spaces.
Received by editor(s): August 25, 2004
Received by editor(s) in revised form: March 8, 2005
Published electronically: February 6, 2006
Additional Notes: The first author was supported by “programa Ramón y Cajal (MCYT)”, and in part by MTM2004-02299 and CURE 2001SGR 00069
Communicated by: Andreas Seeger
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.