We determine the optimal constants in the moment inequalities , 1 ≤ p< q< ∞, where f = (fₙ), g = (gₙ) are two martingales, adapted to the same filtration, satisfying |dgₙ| ≤ |dfₙ|, n = 0,1,2,..., with probability 1. Furthermore, we establish related sharp estimates ||g||₁ ≤ supₙΦ(|fₙ|) + L(Φ), where Φ is an increasing convex function satisfying certain growth conditions and L(Φ) depends only on Φ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-2-1,
author = {Adam Os\k ekowski},
title = {Sharp moment inequalities for differentially subordinated martingales},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {103-131},
zbl = {1207.60034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-2-1}
}
Adam Osękowski. Sharp moment inequalities for differentially subordinated martingales. Studia Mathematica, Tome 196 (2010) pp. 103-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-2-1/