Hsu, Elton P. Logarithmic Sobolev inequalities on path spaces. (Inégalités de Sobolev logarithmiques sur un espace de chemins.) (French) Zbl 0826.46023 C. R. Acad. Sci., Paris, Sér. I 320, No. 8, 1009-1012 (1995). Summary: Suppose that \(W_o(M)\) is the space of paths \(\gamma: [0, 1]\to M\) on a complete connected Riemannian manifold \(M\) of dimension \(n\) such that \(\gamma(0)= o\in M\). We prove a logarithmic Sobolev inequality on \(W_o(M)\): If \(\text{Ric}_M\geq - c\) for a nonnegative constant \(c\), then \[ \int_{W_o(M)} F^2\log |F|d\nu\leq C_M|DF|^2+ |F|^2\log |F| \] with \(C_M\leq (1+ ce^c)^2\). Cited in 1 ReviewCited in 8 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 58D15 Manifolds of mappings Keywords:complete connected Riemannian manifold; logarithmic Sobolev inequality PDFBibTeX XMLCite \textit{E. P. Hsu}, C. R. Acad. Sci., Paris, Sér. I 320, No. 8, 1009--1012 (1995; Zbl 0826.46023)