Kato class measures of symmetric Markov processes under heat kernel estimates (Q996261)
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scientific article; zbMATH DE number 5190797
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Kato class measures of symmetric Markov processes under heat kernel estimates |
scientific article; zbMATH DE number 5190797 |
Statements
Kato class measures of symmetric Markov processes under heat kernel estimates (English)
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13 September 2007
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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.
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Kato class
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Markov process
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heat kernel
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Dynkin class
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semigroup kernel
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resolvent kernel
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Green kernel
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ultracontractivity
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Nash type inequality
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Sobolev inequality
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Brownian motion
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symmetric \(\alpha \)-stable process
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relativistic \(\alpha \)-stable process
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\(d\)-sets
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Riemannian manifolds
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Li-Yau's estimate
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nested fractals
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Sierpinski carpet
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