A remark on perturbation of hyperbounded semigroups for vector valued functions
Masanori Hino · Kyoto journal of mathematics · 1997
P ertu rba tion t h e o r y o f hyperbounded semigroups h a s b e e n u su a lly developed in the framework of L2 space . T o ob ta in essen tia l self adjointness of perturbed infinitesimal generator, potential terms a re often imposed on the condition that their exponentials have every (or large enough) moment. O n th e o th e r h an d , Shigekawa [12] trea ted LP semigroups fo r vector valued functions. He also discussed essential self adjointness of a perturbed generator under the formulation applicable to L P sense. I n t h i s note , w e d is c u s s p e r tu r b a t io n th e o r y f o r (non symmetric) semigroups for vector valued functions which a re controlled by scalar valued hyperbounded semigroups, slightly modifying the setting in [1 2 ]. We give an explicit constant of moment sufficient for the stability of operator cores in Lb sense . T h is constan t is expressed by p and the logarithmic Sobolev constant of the dominating semigroup.