The approximation property of some vector valued Sobolev-Slobodeckij spaces

Traces of vector-valued Sobolev Spaces

The aim of the paper is to characterize the trace space of vector-valued Sobolev spaces W p (R , E) , where E is an arbitrary Banach space. In particular, we do not assume that the underlying Banach space E has the UMD property. Vector-valued Sobolev and Besov spaces are widely used in abstract evolution equations, cf. e.g. Amann [1, 2, 4], Veraar and Weis [57] or Denk, Hieber, Prüss, Saal, and...

On some questions of topology for -valued fractional Sobolev spaces

"&('*),+/.0 1 )213&4 a.e. 576 Our main results assert that is path-connected if 8!" :9 while it has the same homotopy classes as ;=<> *? @ if 8!BA 9 . We also present some results and open problems about density of smooth maps in C D E? F . Sobre algunas cuestiones topológicas para espacios de Sobolev fracionarios con valores en GIH Resumen. El propósito de este artı́culo es describir las clase...

Some Results on p-Best Approximation in Vector Spaces

Pelczyński’s Property (v) on Spaces of Vector-valued Functions

Let E be a separable Banach space and Ω be a compact Hausdorff space. It is shown that the space C(Ω, E) has property (V) if and only if E does. Similar result is also given for Bochner spaces L(μ,E) if 1 < p < ∞ and μ is a finite Borel measure on Ω.

Some Approximation Properties in Musielak-Orlicz-Sobolev Spaces

Some approximation theorems involving the modular convergence, which improve known density results of interest in the existence theory for strongly nonlinear boundary value problems are presented.