INTERMEDIATE SPACES RELATED TO ANALYTIC SEMIGROUPS GENERATED BY ELLIPTIC OPERATORS

Abstract

In this paper, we deal with the theory of interpolation spaces between initial Banach functional spaces and the domain of an elliptic differential operator, which is to be the infinitesimal generator of an analytic semigroup. Based on the theory of basic properties of Besob spaces and characterized by the domain of the infinitesimal generator, we can be applied to L^1-valued control problems or the maximal regularity for the abstract initial value problems in the negative space.