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Sharp inequalities for martingales with values in $\ell_\infty^N$


 
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1. Title Title of document Sharp inequalities for martingales with values in $\ell_\infty^N$
 
2. Creator Author's name, affiliation, country Adam Osękowski; University of Warsaw; Poland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Martingale; transform; UMD space; best constants
 
3. Subject Subject classification 60G42; 60G44
 
4. Description Abstract

The objective of the paper is to study sharp inequalities for transforms of martingales taking values in $\ell_\infty^N$. Using Burkholder's method combined with an intrinsic duality argument, we identify, for each $N\geq 2$, the best constant $C_N$ such that the following holds. If $f$ is a martingale with values in $\ell_\infty^N$ and $g$ is its transform by a sequence of signs, then

$$||g||_1\leq C_N ||f||_\infty.$$

This is closely related to the characterization of UMD spaces in terms of the so-called $\eta$ convexity, studied in the eighties by Burkholder and Lee.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2013-08-09
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2667
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2667
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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