3 problems

For every $1<p\leq\infty$, does there exist a constant $C_p<\infty$, independent of the dimension $d$, such that for every $f\in\ell^p(\mathbb{Z}^d)$,…

Let $p e(1/2,1]$ and let $f:\mathbb{Z}\to\mathbb{R}$ be a function in $ell^{p}(\mathbb{Z})$. Write ${\rm Var}_p f$ for the $p$-variation of $f$, and let $Mf$ denote the centered di…

Let $f\in\ell^2(\mathbb Z)$ and write $e(t)=e^{2\pi i t}$. Pierce's discrete quadratic Carleson conjecture. The inequality … holds. This is a discrete analogue of Stein's maximal q…