A Note on the Burkholder-Rosenthal Inequality

Adam Osękowski

Adam Osękowski

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 60 (2012), p. 177-185 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let df be a Hilbert-space-valued martingale difference sequence. The paper is devoted to a new, elementary proof of the estimate $∥ \sum_{k = 0}^{\infty} d f_{k} ∥_{p} \leq C_{p} ∥ (\sum_{k = 0}^{\infty} (| d f_{k} | ² | ℱ_{k - 1} {))}^{1 / 2} ∥_{p} + ∥ (\sum_{k = 0}^{\infty} | d f_{k} {|^{p})}^{1 / p} ∥_{p},$ with $C_{p} = O (p / l n p)$ as p → ∞.

Publié le : 2012-01-01
EUDML-ID : urn:eudml:doc:281326

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     title = {A Note on the Burkholder-Rosenthal Inequality},
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     volume = {60},
     year = {2012},
     pages = {177-185},
     language = {en},
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Adam Osękowski. A Note on the Burkholder-Rosenthal Inequality. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 60 (2012) pp. 177-185. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-2-7/