Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval

Abstract

We consider various fractional properties of regularity for vector valued functions defined on an interval I. In other words we study the functions in the Sobolev spaces Ws,p(I;E), in the Nikolskii spaces Ns,p(I;E), or in the Besov spaces Bs, pλ(I; E). Theses spaces are defined by integration and translation, and E is a Banach space. In particular we study the dependence on the parameters s, p and λ, that is imbeddings for different parameters. Moreover we compare each space to the others, and we give Lipschits continuity, existence of traces and q-integrability properties. These results rely only on integration techniques. © 1990 Fondazione Annali di Matematica Pura ed Applicata.