Suppose f = (fₙ), g = (gₙ) are martingales with respect to the same filtration, satisfying , n = 1,2,..., with probability 1. Under some assumptions on f₀, g₀ and an additional condition that one of the processes is nonnegative, some sharp inequalities between the pth norms of f and g, 0 < p < ∞, are established. As an application, related sharp inequalities for stochastic integrals and harmonic functions are obtained.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-4-9,
author = {Adam Os\k ekowski},
title = {Sharp Norm Inequalities for Martingales and their Differential Subordinates},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {55},
year = {2007},
pages = {373-385},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-4-9}
}
Adam Osękowski. Sharp Norm Inequalities for Martingales and their Differential Subordinates. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 373-385. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-4-9/