Rothaus, O. S. Logarithmic Sobolev inequalities and the growth of \(L^{p}\) norms. (English) Zbl 0896.46021 Proc. Am. Math. Soc. 126, No. 8, 2309-2314 (1998). 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. Cited in 6 Documents 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 Keywords:exponential integrability of Lip 1 functions; logarithmic Sobolev inequality; fundamental estimates of the growth of \(L^p\) norms PDFBibTeX XMLCite \textit{O. S. Rothaus}, Proc. Am. Math. Soc. 126, No. 8, 2309--2314 (1998; Zbl 0896.46021) Full Text: DOI