Feller semigroups, $L^p$-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definit symbols

by    W. Farkas, N. Jacob, R.L. Schilling

Preprint series: 99-15, Analysis

47D07 Markov semigroups, {For Markov processes, See 60Jxx}
31C25 Dirichlet spaces
60J35 Transition functions, generators and resolvents, See Also {47D03, 47D07}
35S99 None of the above but in this section

Abstract: Interpolation of $L^2$-sub-Markovian semigroups which are also Feller semigroups is investigated.
Subordination in the sense of Bochner is used to discuss refinements of $L^p$-sub-Markovian semigroups.
We prove also that if an operator extends to an $L^p$-Dirichlet operator for all $p\ge p_0$, then it has to satisfy the positive maximum principle.
Some applications to pseudo-differential operators with negative definite symbols are presented.

Keywords: $L^p$-sub-Markovian semigroups, Feller semigroups, positive maximum principle, Dirichlet operators, $(r,p)$-capacities

Upload: 1999-03-03

Update: 1999-03-08

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