Kato class measures of symmetric Markov processes under heat kernel estimates
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.
scientific article; zbMATH DE number 5190797
scientific article