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ON SHARP SOBOLEV EMBEDDING AND THE LOGARITHMIC SOBOLEV INEQUALITY

Published online by Cambridge University Press:  01 January 1998

WILLIAM BECKNER  and
MICHAEL PEARSON
WILLIAM BECKNER
Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA
MICHAEL PEARSON
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA
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Abstract

The purpose of this note is to give a short proof of the Gross logarithmic Sobolev inequality using the asymptotics of the sharp L2 Sobolev constant and the product structure of Euclidean space. Let F∈Lr(IRn) for some positive r with ∥F∥r=1.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 1 , January 1998 , pp. 80 - 84
Copyright
© The London Mathematical Society 1998

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