Sharp LlogL inequalities for differentially subordinated martingales and harmonic functions

Oşekowski, Adam

Illinois J. Math., Tome 52 (2008) no. 1, p. 745-756 / Harvested from Project Euclid

Résumé

Let (x_n), (y_n) be two martingales adapted to the same filtration $(\mathcal{F}_{n})$ satisfying, with probability 1, ¶ |dx_n|≤|dy_n|, n=0, 1, 2, …. ¶ For every K>0, we determine the best constant L=L(K) for which the inequality ¶ \[\mathbb{E}|x_{n}|\leq K\mathbb{E}|y_{n}|\log|y_{n}|+L,\quad n=0,1,2,\ldots \] ¶ holds true. We also prove a similar inequality for harmonic functions.

Publié le : 2008-05-15
Classification: 60G42, 31B05

@article{1254403712,
     author = {Osekowski, Adam},
     title = {Sharp LlogL inequalities for differentially subordinated martingales and harmonic functions},
     journal = {Illinois J. Math.},
     volume = {52},
     number = {1},
     year = {2008},
     pages = { 745-756},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1254403712}
}

Oşekowski, Adam. Sharp LlogL inequalities for differentially subordinated martingales and harmonic functions. Illinois J. Math., Tome 52 (2008) no. 1, pp.  745-756. http://gdmltest.u-ga.fr/item/1254403712/