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October, 1977 A Square Function Inequality
G. Klincsek
Ann. Probab. 5(5): 823-825 (October, 1977). DOI: 10.1214/aop/1176995727

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 $\|Mf\|_p \leqq p\|Sf\|_p$.

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G. Klincsek. "A Square Function Inequality." Ann. Probab. 5 (5) 823 - 825, October, 1977. https://doi.org/10.1214/aop/1176995727

Information

Published: October, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0375.60064
MathSciNet: MR455111
Digital Object Identifier: 10.1214/aop/1176995727

Subjects:
Primary: 60G45
Secondary: 60H05

Keywords: martingale , maximal function , square function

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 5 • October, 1977
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