On Solvability of Parabolic Functional Differential Equations in Banach Spaces (II)

Abstract

In this paper, a parabolic functional differential equation is considered in the spaces C(0, T ;Hs p(Q)) for s close to 1 and p close to 2. The transformations of the space argument are supposed to be bounded in the spaces Hs p(Q) with small smoothness exponent and p close to 2. The corresponding resolvent estimate of the elliptic part of the operator is obtained in order to show that it generates a strongly continuous semigroup.