Kato class measures of symmetric Markov processes under heat kernel estimates

DOI10.1016/j.jfa.2006.10.010zbMath1132.47033OpenAlexW2077497291WikidataQ124850832 ScholiaQ124850832MaRDI QIDQ996261

Kazuhiro Kuwae, Masayuki Takahashi

Publication date: 13 September 2007

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2006.10.010

zbMATH Keywords

Brownian motionresolvent kernelRiemannian manifoldsMarkov processSierpinski carpetheat kernelSobolev inequalityKato classultracontractivityGreen kernel\(d\)-setssymmetric \(\alpha \)-stable processDynkin classnested fractalsrelativistic \(\alpha \)-stable processLi-Yau's estimateNash type inequalitysemigroup kernel

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Markov semigroups and applications to diffusion processes (47D07) Diffusion processes (60J60) Probabilistic potential theory (60J45)

Related Items (28)

A Feynman-Kac-Itô formula for magnetic Schrödinger operators on graphs ⋮ On a positivity preservation property for Schrödinger operators on Riemannian manifolds ⋮ Large deviation principles for generalized Feynman-Kac functionals and its applications ⋮ A refinement of analytic characterizations of gaugeability for generalized Feynman-Kac functionals ⋮ Spread rate of branching Brownian motions ⋮ \(L^p\)-Kato class measures for symmetric Markov processes under heat kernel estimates ⋮ Path integrals and the essential self-adjointness of differential operators on noncompact manifolds ⋮ Kato classes for Lévy processes ⋮ Functions with bounded variation on a class of Riemannian manifolds with Ricci curvature unbounded from below ⋮ On the geometry of semiclassical limits on Dirichlet spaces ⋮ \(L^p\)-independence of spectral radius for generalized Feynman-Kac semigroups ⋮ On a construction of harmonic function for recurrent relativistic \(\alpha\)-stable processes ⋮ The Kato class on compact manifolds with integral bounds on the negative part of Ricci curvature ⋮ On generalized Schrödinger semigroups ⋮ Large deviations for symmetric stable processes with Feynman-Kac functionals and its application to pinned polymers ⋮ Molecules as metric measure spaces with Kato-bounded Ricci curvature ⋮ Analytic characterizations of gaugeability for generalized Feynman-Kac functionals ⋮ Feynman-Kac penalization problem for additive functionals with jumping functions ⋮ Feynman-Kac penalizations of rotationally symmetric \(\alpha\)-stable processes ⋮ Kato’s inequality and form boundedness of Kato potentials on arbitrary Riemannian manifolds ⋮ Heat kernels in the context of Kato potentials on arbitrary manifolds ⋮ General analytic characterization of gaugeability for Feynman-Kac functionals ⋮ \(L^p\)-independence of spectral bounds of Feynman-Kac semigroups by continuous additive functionals ⋮ Perturbation theory for convolution semigroups ⋮ \(L^p\)-Kato class measures and their relations with Sobolev embedding theorems for Dirichlet spaces ⋮ Generalized Schrödinger semigroups on infinite graphs ⋮ On general perturbations of symmetric Markov processes ⋮ ON A SUFFICIENT CONDITION FOR LARGE DEVIATIONS OF ADDITIVE FUNCTIONALS

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