Some inequalities for sub-Markovian generators and their applications to the perturbation theory

Abstract

We characterize the domain in L p {L^p} -space of generators of submarkovian semigroups in terms of the form domain in L 2 {L^2} and give the corresponding inequality. Using this inequality we obtain a criterion for the formal difference A − B A - B of such generators to be a generator of a contraction semigroup in L p {L^p} . The conditions on perturbation are expressed in terms of forms, i.e., in L 2 {L^2} -terms.