On coercive solvability of parabolic equations

In this paper we study the coercive solvability of abstract differential equations of parabolic type in the spaces of L. N. Slobodetskii $W_p^\alpha$. It is established that the solution of equations with a constant operator $A$ which generates an analytic semigroup belongs to the trace space $E(\alpha,p,A)$. The results obtained are applied to the study of equations with a variable operator.