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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Factoring Sobolev inequalities through classes of functions


Authors: David Alonso-Gutiérrez, Jesús Bastero and Julio Bernués
Journal: Proc. Amer. Math. Soc. 140 (2012), 3557-3566
MSC (2010): Primary 46E35; Secondary 46E30, 26D10, 52A40
Published electronically: February 24, 2012
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Abstract: We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools from Convex Geometry. In this paper we prove a (sharp) connection between them.


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Additional Information

David Alonso-Gutiérrez
Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
Email: daalonso@unizar.es

Jesús Bastero
Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
Email: bastero@unizar.es

Julio Bernués
Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
Email: bernues@unizar.es

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11355-3
PII: S 0002-9939(2012)11355-3
Keywords: Sobolev inequality, sharp constants, affine isoperimetric inequalities
Received by editor(s): October 20, 2010
Received by editor(s) in revised form: April 15, 2011
Published electronically: February 24, 2012
Additional Notes: The three authors were partially supported by MCYT Grant(Spain) MTM2010-16679 and DGA E-64
Communicated by: Marius Junge
Article copyright: © Copyright 2012 American Mathematical Society