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

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Principle of Local Reflexivity

I cannot comment above, so I have to write another answer. To clarify for you Rafael why such an $i$ exists in Bill's comment. Take the same setup, $\xi\in\mathbb{K}^N$ such that \begin{equation}\un …
Keaton Hamm's user avatar
7 votes
1 answer
509 views

Multivariate Maximal Hilbert Transform

One way to define the maximal Hilbert transform of a function, $f$, is by $$\mathcal{H}[f](x):=\sup_{\varepsilon>0} \left| \int_{|x-t|\geq\varepsilon} \frac{f(t)}{x-t} \, dt\right|, \quad x\in\mathbb{ …
Keaton Hamm's user avatar