by W. Farkas, N. Jacob, R.L. Schilling
Preprint series: 99-15, Analysis
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