The Annals of Probability

A Square Function Inequality

G. Klincsek

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Abstract

For martingales $f \in L_p (2 \leqq p < \infty)$ the inequality $\|Mf\|_p \leqq (p + 1)\|Sf\|_p$ is proved, where $Mf = \sup_n |f_n|$ is the maximal function and $S^2 = \sum_n |f_n - f_{n-1}|^2$ the martingale square function. For integer $p$ the estimate becomes $\|Mf\|_p \leqq p\|Sf\|_p$.

Article information

Source
Ann. Probab., Volume 5, Number 5 (1977), 823-825.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995727

Digital Object Identifier
doi:10.1214/aop/1176995727

Mathematical Reviews number (MathSciNet)
MR455111

Zentralblatt MATH identifier
0375.60064

JSTOR
links.jstor.org

Subjects
Primary: 60G45
Secondary: 60H05: Stochastic integrals

Keywords
Martingale maximal function square function

Citation

Klincsek, G. A Square Function Inequality. Ann. Probab. 5 (1977), no. 5, 823--825. doi:10.1214/aop/1176995727. https://projecteuclid.org/euclid.aop/1176995727


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