1
vote
0answers
54 views

Is $\partial^\alpha$ a map $H^{s,p}(\mathbb R^N,F)\to H^{s-|\alpha|,p}(\mathbb R^N,F)$?

More precisely, the question is formulated as follows. Let $F$ be an arbitrary Banach space, especially not having the UMD−property. Let $N\in\mathbb N$ and $s\in\mathbb R$ and $1\le p\le +\infty$ . ...
2
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1answer
253 views

Projections in Sobolev spaces

I was browsing through the literature but I have not found anything related to my question: I am interested in decompositions of functions in Sobolev spaces $W^{k,p}(\Omega)$, where $\Omega$ is some ...