3 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…

Improved jump inequality. For $\frac{n}{n+1}<p\leq 1$, there exists $C_p>0$ such that

Let $d4b7$ be a variation function, and let the Loève–Young inequality refer to an inequality controlling the integral of a product in terms of the $d4b7$-variations of the integra…