5 votes

Possible research directions in analysis?

I find that students often come in with these kinds of ideas, that almost everything is known, it's hard to do anything, the problems are mostly solved. Then they ask how to best position themselves ...
user378654's user avatar
5 votes

A fractional weighted Poincaré inequality

It is not true. Start with a function $u$ which vanishes for $x<0$ and is equal to $1$ for $0 \leq x \leq \frac 12$ and then smooth from $x \geq \frac 12$. The Fourier coefficients behave like $1/n$...
Giorgio Metafune's user avatar
4 votes

Any references for generalised square functions?

For $0<p<\infty$, $0<q\le\infty$ and $s\in\mathbb R$, the Triebel-Lizorkin space $F_{pq}^s(\mathbb R^n)$ is the set of all (tempered distributions) $f$ such that $\big\||\{2^{js}\cdot P_jf\}...
Liding Yao's user avatar
3 votes

Question regarding proof of Littlewood-Paley

Apologies if I've misunderstood the question; Grafakos comments in this paragraph that The fundamental ingredient in the proof is that $f=\sum_{\mathbf{j}\in\mathbb{Z}^n}\Delta_\mathbf{j}^\#\Delta_\...
Ben Johnsrude's user avatar

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