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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.

##### MSC:
 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 4.6e+41 Spaces of vector- and operator-valued functions
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