Timeline for $H^s(\mathbb T)$ is a Banach algebra for $s>1/2$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 10, 2014 at 10:22 | comment | added | Jean Van Schaftingen | This holds for a compact manifold: by Adams and local charts, the result holds on a neighbourhood of any point, and the manifold can be covered by finitely many such neighbourhoods. This should also work for manifolds with some “bounded geometry”. | |
| Jun 10, 2014 at 9:35 | comment | added | Delio Mugnolo | But 7.57 is an imbedding result for Sobolev spaces on domains of $\mathbb R^n$! How does this implies the claimed property? I have checked a bit in the literature: It seems that Thm. 3.5 in Sobolev spaces on Riemannian manifolds by E. Hebey settles my question. | |
| Jun 10, 2014 at 3:49 | comment | added | Jean Van Schaftingen | Adams, Sobolev spaces, Academic Press, 1975, theorem 7.57 | |
| Jun 10, 2014 at 3:48 | history | edited | Jean Van Schaftingen | CC BY-SA 3.0 |
Additional reference
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| Jun 7, 2014 at 13:31 | comment | added | Delio Mugnolo | Can you provide a reference for your last assertion? Does one have that $W^{s,p}(M)\hookrightarrow L^\infty(M)$ if $sp>{\rm dim } M$? | |
| Jun 6, 2014 at 13:12 | history | answered | Jean Van Schaftingen | CC BY-SA 3.0 |