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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
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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:

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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


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