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 Ws,p(I;E), in the Nikolskii spaces Ns,p(I;E), or in the Besov spaces B λ s, p (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.
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Simon, J. Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval. Annali di Matematica pura ed applicata 157, 117–148 (1990). https://doi.org/10.1007/BF01765315
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DOI: https://doi.org/10.1007/BF01765315