2 problems

Let $p e(1/2,1]$ and let $f:\mathbb{Z}tomathbb{R}$ 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 discrete…

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…