Note on a Square Function Inequality
Pittenger, A. O.
Ann. Probab., Tome 7 (1979) no. 6, p. 907-908 / Harvested from Project Euclid
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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 $\|M\|_p \leqslant p\|V\|_p$.
Publié le : 1979-10-14
Classification:  Martingale,  maximal function,  square function,  60G45,  60H05 
@article{1176994952,
     author = {Pittenger, A. O.},
     title = {Note on a Square Function Inequality},
     journal = {Ann. Probab.},
     volume = {7},
     number = {6},
     year = {1979},
     pages = { 907-908},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176994952}
}

Pittenger, A. O. Note on a Square Function Inequality. Ann. Probab., Tome 7 (1979) no. 6, pp.  907-908. http://gdmltest.u-ga.fr/item/1176994952/