A Martingale Inequality for the Square and Maximal Functions
Chen, Louis H. Y.
Ann. Probab., Tome 7 (1979) no. 6, p. 1051-1055 / Harvested from Project Euclid
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An inequality for certain random sequences more general than martingales or nonnegative submartingales is proved. Three special cases are deduced, one of which generalizes and refines a result of Austin. As an application of the inequality, the special cases are used to give new proofs of Burkholder's $L \log L$ and $L_p$ (for $1 < p \leqslant 2$) inequalities for the square function of a martingale or a nonnegative submartingale.
Publié le : 1979-12-14
Classification:  Martingale inequality,  maximal function,  square function,  weak martingale,  60G45 
@article{1176994898,
     author = {Chen, Louis H. Y.},
     title = {A Martingale Inequality for the Square and Maximal Functions},
     journal = {Ann. Probab.},
     volume = {7},
     number = {6},
     year = {1979},
     pages = { 1051-1055},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176994898}
}

Chen, Louis H. Y. A Martingale Inequality for the Square and Maximal Functions. Ann. Probab., Tome 7 (1979) no. 6, pp.  1051-1055. http://gdmltest.u-ga.fr/item/1176994898/