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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A proof of the Burkholder theorem for martingale transforms


Author: T. Shintani
Journal: Proc. Amer. Math. Soc. 82 (1981), 278-279
MSC: Primary 60G42
DOI: https://doi.org/10.1090/S0002-9939-1981-0609666-2
MathSciNet review: 609666
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Abstract: If $ g$ is the transform of an $ {L^1}$-bounded martingale $ f$ under a predictable sequence $ \upsilon $ satisfying $ {\text{sup}_n}\left\vert {{\upsilon _n}} \right\vert < \infty $ almost everywhere, then a proof of the convergence of $ g$ is given using an approximation of $ f$ by a martingale of bounded variation.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0609666-2
Keywords: Martingale, almost everywhere convergence, bounded variation, approximation, Burkholder transform, Banach space
Article copyright: © Copyright 1981 American Mathematical Society