# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## Sharp Norm Inequalities for Martingales and their Differential Subordinates

### Tom 55 / 2007

Bulletin Polish Acad. Sci. Math. 55 (2007), 373-385 MSC: Partially supported by MEiN Grant 1 PO3A 012 29. DOI: 10.4064/ba55-4-9

#### Streszczenie

Suppose $f=(f_n)$, $g=(g_n)$ are martingales with respect to the same filtration, satisfying $$|f_n-f_{n-1}| \leq |g_n-g_{n-1}|,\quad \ n=1,2,\ldots,$$ with probability $1$. Under some assumptions on $f_0$, $g_0$ and an additional condition that one of the processes is nonnegative, some sharp inequalities between the $p$th norms of $f$ and $g$, $0< p< \infty$, are established. As an application, related sharp inequalities for stochastic integrals and harmonic functions are obtained.

#### Autorzy

• Adam Os/ekowskiDepartment of Mathematics, Informatics and Mechanics
Warsaw University
Banacha 2
02-097 Warszawa, Poland
e-mail

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