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October, 1979 Note on a Square Function Inequality
A. O. Pittenger
Ann. Probab. 7(5): 907-908 (October, 1979). DOI: 10.1214/aop/1176994952

Abstract

Let $X$ be an $L_p$ martingale, $3 \leqslant p < \infty$. Let $M = \sup|X_k|$ and $V^2 = \Sigma(X_k - X_{k-1})^2$. We show that $\|X\|_p \leqslant (p - 1)\|V\|_p$ and, consequently, that $\|M\|_p \leqslant p\|V\|_p$.

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A. O. Pittenger. "Note on a Square Function Inequality." Ann. Probab. 7 (5) 907 - 908, October, 1979. https://doi.org/10.1214/aop/1176994952

Information

Published: October, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0414.60052
MathSciNet: MR542143
Digital Object Identifier: 10.1214/aop/1176994952

Subjects:
Primary: 60G45
Secondary: 60H05

Keywords: martingale , maximal function , square function

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 5 • October, 1979
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