FRACTIONAL POWERS AND INTERPOLATION THEORY FOR MULTIVARIATE LINEAR OPERATORS AND APPLICATIONS

We provide intermediate properties for the domains of the fractional powers of an abstract multivalued linear operator A of weak parabolic type. In particular, the results exhibit the special role played by the linear subspace A0. The behaviour of the singular semigroup generated by A with respect to the domains of the fractional powers is then studied. Such results are applied to maximal time and space regularity for solutions to abstract multivalued evolution equations. Some concrete cases of partial differential equations enlighten the abstract results.