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Logarithmic Sobolev inequalities and the growth of \(L^{p}\) norms. (English) Zbl 0896.46021

Summary: 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.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
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