Kato class measures of symmetric Markov processes under heat kernel estimates
type: Item
instance of: scholarly article
title: Kato class measures of symmetric Markov processes under heat kernel estimates
zbMATH Open document ID: 1132.47033
author: Kazuhiro Kuwae
author: Masayuki Takahashi
published in: Journal of Functional Analysis
publication date: 2007-09-13T00:00:00Z
review text: Two classes of Kato class measures, defined by the heat kernel and the Green function, respectively, are identified for symmetric Markov processes on a locally compact metric space with certain heat kernel upper and lower bounds. Uniform boundedness of integrals on balls with fixed radius over measures in the Kato class is proved. Some concrete examples are provided to illustrate the range of applications of the main results.
reviewed by: Feng-Yu Wang
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60J25
zbMATH DE Number: 5190797
zbMATH Keywords: Kato class
zbMATH Keywords: Markov process
zbMATH Keywords: heat kernel
zbMATH Keywords: Dynkin class
zbMATH Keywords: semigroup kernel
zbMATH Keywords: resolvent kernel
zbMATH Keywords: Green kernel
zbMATH Keywords: ultracontractivity
zbMATH Keywords: Nash type inequality
zbMATH Keywords: Sobolev inequality
zbMATH Keywords: Brownian motion
zbMATH Keywords: symmetric \(\alpha \)-stable process
zbMATH Keywords: relativistic \(\alpha \)-stable process
zbMATH Keywords: \(d\)-sets
zbMATH Keywords: Riemannian manifolds
zbMATH Keywords: Li-Yau's estimate
zbMATH Keywords: nested fractals
zbMATH Keywords: Sierpinski carpet
MaRDI profile type: Publication
full work available at URL: j.jfa.2006.10.010
OpenAlex ID: W2077497291
Wikidata QID: Q124850832
cites work: Brownian motion and harnack inequality for Schrödinger operators
cites work: Additive functionals, nowhere Radon and Kato class smooth measures associated with Dirichlet forms
cites work: Brownian Motion and Harmonic Analysis on Sierpinski Carpets
cites work: Asymptotic formulas for symmetric stable semigroups
cites work: Some Theorems on Stable Processes
cites work: Heat kernel estimates for stable-like processes on \(d\)-sets.
cites work: From Brownian Motion to Schrödinger’s Equation
cites work: Some isoperimetric inequalities and eigenvalue estimates
cites work: Asymptotic behaviour of densities of stable semigroups of measures
cites work: Transition density estimates for Brownian motion on affine nested fractals
cites work: Dirichlet forms and symmetric Markov processes
cites work: Pointwise estimates for densities of stable semigroups of measures
cites work: Q3769668
cites work: Q4453424
cites work: Q5484092
cites work: Heat kernels on metric measure spaces and an application to semilinear elliptic equations
cites work: Optimal Sobolev Inequalities on Complete Riemannian Manifolds with Ricci Curvature Bounded Below and Positive Injectivity Radius
cites work: Perturbation of Translation Invariant Positivity Preserving Semigroups on L 2 (R N )
cites work: NASH-TYPE INEQUALITIES AND HEAT KERNELS FOR NON-LOCAL DIRICHLET FORMS
cites work: Schrödinger operators with singular potentials
cites work: Remarks on Schrödinger operators with vector potentials
cites work: Estimates of transition densities for Brownian motion of nested fractals
cites work: Q3437157
cites work: Analysis.
cites work: The First Hitting Distribution of a Sphere for Symmetric Stable Processes
cites work: Estimates of Green function for relativistic \(\alpha\)-stable process
cites work: Uniformly elliptic operators on Riemannian manifolds
cites work: Aspects of Sobolev-type inequalities
cites work: Schrödinger operators in the twentieth century
cites work: Subcriticality and gaugeability for symmetric [alpha]-stable processes
cites work: A probabilistic principle and generalized Schrödinger perturbation
DOI: 10.1016/J.JFA.2006.10.010
description: scientific article; zbMATH DE number 5190797