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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
0
votes
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 …
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{ …