Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Logarithmic Sobolev inequalities and the growth of $L^{p}$ norms

Author(s): O. S. Rothaus
Journal: Proc. Amer. Math. Soc. 126 (1998), 2309-2314.
MSC (1991): Primary 46E35, 46E39
MathSciNet review: 1452824
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We show that many of the recent results on exponential integrability of Lip 1 functions, when a logarithmic Sobolev inequality holds, follow from more fundamental estimates of the growth of $L^{p}$ norms under the same hypotheses.

References:

1.: Aida, S., Masuda, T., and Shigekawa, I., Logarithmic Sobolev Inequalities and Exponential Integrability, J. of Funct. Anal. 126 (1994), 83-101. MR 95m:60111
2.: Aida, S. and Stroock, D., Moment estimates derived from Poincaré and logarithmic Sobolev inequalities, Math. Res. Lett. 1 (1994), 75-86. MR 95f:60086
3.: Davies, E.B. and Simon, B., Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. of Funct. Anal. 59 (1984), 335-395. MR 86e:47054
4.: Ledoux, M., Remarks on Logarithmic Sobolev Constants, Exponential Integrability, and Bounds on the Diameter, J. Math. Kyoto Univ. 35 (1995), 211-220. CMP 95:17

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|