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Results tagged with sobolev-spaces
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user 766
A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
22
votes
Accepted
Compactness in Sobolev spaces
No. As a general rule, in order to obtain compactness in some norm, one needs control of a higher regularity than what is associated to that norm, in order to shut down an "escape to frequency infini …
- 114k
22
votes
Accepted
When to use more exciting function spaces than ordinary Sobolev spaces?
Spatial weights would be relevant in non-homogeneous settings in which one expects the behaviour at different regions of space to be different. For instance, if there is an obstacle or a boundary, a …
- 114k
9
votes
Does anyone know what is the right reference for the following simple lemma from harmonic an...
This inequality is also a corollary of the main result of
Fefferman, Charles; Stein, Elias M., Some maximal inequalities, Am. J. Math. 93, 107-115 (1971). ZBL0222.26019.
which asserts that
$$ \| \s …
- 114k
9
votes
Accepted
Endpoint Calderon-Zygmund inequality of nonlocal fractional laplacian
I think the estimate is false, at least for $n=1$ and $0 < s < 1/2$, due to the non-locality you mention (I imagine similar arguments would work in other non-local cases). If it held, then one would …
- 114k