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 ...
- 664
5
votes
Accepted
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 $1/n$...
- 4,765
4
votes
Accepted
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\}...
- 786
3
votes
Accepted
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_\...
- 354
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