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Results tagged with fa.functional-analysis
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user 4281
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
0
votes
0
answers
102
views
Must the Lebesgue measure of a $\rho$ - neighbourhood of an $(n-2)$ - dimensional set be at ...
The Lebesgue measure of a $\rho$-neighbourhood of a point in $\mathbb{R}^2$ is of course equal to $c\rho^2$. Similar such considerations in higher dimensions lead me to the following question:
Given …
- 1,771
4
votes
2
answers
2k
views
Inclusions of $C^{k,\alpha}$ spaces
When is $C^{k,\alpha}(\bar{\Omega})$ a
subset of
$C^{k',\alpha'}(\bar{\Omega})$?
Gilbarg and Trudinger says that "for the domains of interest in this work the inclusion will hold whenever $k …
- 1,771
5
votes
1
answer
135
views
Reference for higher order Campanato Lemmas, e.g. `Sufficiently fast L^2 decay on balls to a...
Whence can I reference the following fact (I have seen it quoted as `standard' in respectable places, so I hope it is so)?:
Let $f : B_2(0) \to \mathbb{R}$, say $f \in L^2(B_2(0))$ . Suppose that the …
- 1,771
11
votes
Learning roadmap for harmonic analysis
To my mind, the classical subject is quite different from the modern, evolved form of the subject
I started on the classical side with Yitzhak Katznelson's An Introduction to Harmonic Analysis: This …