Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval. (English) Zbl 0727.46018

Summary: 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 \(W^{s,p}(I;E)\), in the Nikolskii spaces \(N^{s,p}(I;E)\), or in the Besov spaces \(B_{\lambda}^{s,p}(I;E)\). These 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 \(\lambda\), that is imbeddings for different parameters. Moreover we compare each space to the others, and we give Lipschitz continuity, existence of traces and q-integrability properties. These results rely only on integration techniques.


46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E40 Spaces of vector- and operator-valued functions
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