Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces

DOI10.1006/jfan.2000.3592zbMath0968.58026OpenAlexW2036257568MaRDI QIDQ1577669

Shigeki Aida

Publication date: 11 September 2001

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2000.3592

zbMATH Keywords

logarithmic Sobolev inequalitydiffusion processesloop spaceslogarithmic derivatives

Mathematics Subject Classification ID

Brownian motion (60J65) Diffusion processes and stochastic analysis on manifolds (58J65) Manifolds of mappings (58D15)

Related Items (14)

A class of processes on the path space over a compact Riemannian manifold with unbounded diffusion ⋮ Martingale representation and logarithmic-Sobolev inequality for the fractional Ornstein-Uhlenbeck measure ⋮ Characterizations of the upper bound of Bakry-Emery curvature ⋮ Asymptotics of spectral gaps on loop spaces over a class of Riemannian manifolds ⋮ Log-Hessian and deviation bounds for Markov semi-groups, and regularization effect in \(\mathbb{L}^1 \) ⋮ Logarithmic heat kernel estimates without curvature restrictions ⋮ Absence of spectral gaps on a class of loop spaces ⋮ Local spectral gaps on loop spaces. ⋮ Quasi-regular Dirichlet forms on Riemannian path and loop spaces ⋮ A concrete estimate for the weak Poincaré inequality on loop space ⋮ An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups ⋮ A Poincaré inequality on loop spaces ⋮ Functional inequality on path space over a non-compact Riemannian manifold ⋮ On the semimartingale property of Brownian bridges on complete manifolds

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