A Square Function Inequality
Klincsek, G.
Ann. Probab., Tome 5 (1977) no. 6, p. 823-825 / Harvested from Project Euclid
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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 $\|Mf\|_p \leqq p\|Sf\|_p$.
Publié le : 1977-10-14
Classification:  Martingale,  maximal function,  square function,  60G45,  60H05 
@article{1176995727,
     author = {Klincsek, G.},
     title = {A Square Function Inequality},
     journal = {Ann. Probab.},
     volume = {5},
     number = {6},
     year = {1977},
     pages = { 823-825},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995727}
}

Klincsek, G. A Square Function Inequality. Ann. Probab., Tome 5 (1977) no. 6, pp.  823-825. http://gdmltest.u-ga.fr/item/1176995727/