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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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 …
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 …
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 …
Amitesh Datta's user avatar
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 …