All Questions

Suppose $\sum_{\xi \in \mathbb{Z}^d}{a_{\xi}}e^{i\langle x, \xi\rangle }$ converges spherically pointwise to $0$ for all $x \in \mathbb{T}^d$, i.e. $\lim_{R \to \infty} \sum_{|\xi| < R}{a_{\xi}}e^{...

Assume for simplicity that sets $A_i\subset\mathbb{R}$ are compact. If $A_1$ and $A_2$ have positive length, then $A_1+A_2$ contains an interval. That is a variant of the classical Steinhaus theorem ...

in the paper, ON KAKEYA MAPS WITH REGULARITY ASSUMPTIONS, the author of the paper consider the Kakeya conjecture with some regularity on Kakeya map, Kekeya conjecture[Hausdorff dimension version] If ...