On solvability of parabolic functional differential equations in banach spaces (II)

In this paper, a parabolic functional differential equation is considered in the spaces for s close to 1 and p close to 2. The transformations of the space argument are supposed to be bounded in the spaces 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. © 2020, L.N. Gumilyov Eurasian National University.