Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-20T10:12:17.673Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)