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A note on Coulhon type inequalities

Authors: Joaquim Martín and Mario Milman
Journal: Proc. Amer. Math. Soc. 142 (2014), 4221-4237
MSC (2010): Primary 46E30, 26D10
Published electronically: August 6, 2014
MathSciNet review: 3266991
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Abstract: T. Coulhon introduced an interesting reformulation of the usual Sobolev inequalities. We characterize Coulhon type inequalities in terms of rearrangement inequalities.

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Additional Information

Joaquim Martín
Affiliation: Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain

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

Keywords: Sobolev inequalities, modulus of continuity, symmetrization, isoperimetric inequalities, interpolation
Received by editor(s): June 8, 2012
Received by editor(s) in revised form: January 11, 2013
Published electronically: August 6, 2014
Additional Notes: The first author was supported in part by Grants MTM2010-14946, MTM-2010-16232
The work of the second author was partially supported by a grant from the Simons Foundation (#207929).
Communicated by: Richard Rochberg
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.