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

 

A Brascamp-Lieb-Luttinger-type inequality and applications to symmetric stable processes


Authors: Rodrigo Bañuelos, Rafal Latala and Pedro J. Méndez-Hernández
Journal: Proc. Amer. Math. Soc. 129 (2001), 2997-3008
MSC (1991): Primary 30C45
Published electronically: April 17, 2001
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Abstract:

We derive an inequality for multiple integrals from which we conclude various generalized isoperimetric inequalities for Brownian motion and symmetric stable processes in convex domains of fixed inradius. Our multiple integral inequality is a replacement for the classical inequality of H. J. Brascamp, E. H. Lieb and J. M. Luttinger, where instead of fixing the volume of the domain one fixes its inradius.


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Additional Information

Rodrigo Bañuelos
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: banuelos@math.purdue.edu

Rafal Latala
Affiliation: Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Email: rlatala@mimuw.edu.pl

Pedro J. Méndez-Hernández
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: mendez@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06137-8
PII: S 0002-9939(01)06137-8
Keywords: Symmetric stable processes, generalized isoperimetric inequalities, inradius
Received by editor(s): February 29, 2000
Published electronically: April 17, 2001
Additional Notes: The first author was supported in part by NSF grant # 9700585-DMS
The second author was supported in part by KBN grant # 2 PO3 043 15
The third author was supported in part by Purdue Research Foundation grant # 690-1395-3149
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2001 American Mathematical Society