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Sobolev spaces of vector-valued functions | Iván Caamaño
; Jesús A. Jaramillo
; Ángeles Prieto
; Alberto Ruiz de Alarcón
; | Date: |
7 Aug 2020 | Abstract: | We are concerned here with Sobolev-type spaces of vector-valued functions.
For an open subset $Omegasubsetmathbb{R}^N$ and a Banach space $V$, we
compare the classical Sobolev space $W^{1,p}(Omega, V)$ with the so-called
Sobolev-Reshetnyak space $R^{1,p}(Omega, V)$. We see that, in general,
$W^{1,p}(Omega, V)$ is a closed subspace of $R^{1,p}(Omega, V)$. As a main
result, we obtain that $W^{1,p}(Omega, V)=R^{1,p}(Omega, V)$ if, and only if,
the Banach space $V$ has the Radon-Nikod’ym property | Source: | arXiv, 2008.03040 | Services: | Forum | Review | PDF | Favorites |
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