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Symmetrization inequalities and Sobolev embeddings
Author(s):
Joaquim
Martín;
Mario
Milman
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2335-2347.
MSC (2000):
Primary 46E30, 26D10
Posted:
February 6, 2006
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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
Email:
jmartin@mat.uab.es
Mario
Milman
Affiliation:
Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431
Email:
interpol@bellsouth.net
DOI:
10.1090/S0002-9939-06-08277-3
PII:
S 0002-9939(06)08277-3
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
Posted:
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
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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