Sharp weak type inequalities for the Haar system and related estimates for nonsymmetric martingale transforms

Author:
Adam Osȩkowski

Journal:
Proc. Amer. Math. Soc. **140** (2012), 2513-2526

MSC (2010):
Primary 60G42; Secondary 60G44

DOI:
https://doi.org/10.1090/S0002-9939-2011-11093-1

Published electronically:
November 8, 2011

MathSciNet review:
2898713

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Abstract | References | Similar Articles | Additional Information

Abstract: For any , we determine the optimal constant such that the following holds. If is the Haar system, then for any vectors from a separable Hilbert space and , , we have

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Additional Information

**Adam Osȩkowski**

Affiliation:
Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland

Email:
ados@mimuw.edu.pl

DOI:
https://doi.org/10.1090/S0002-9939-2011-11093-1

Keywords:
Martingale,
martingale transform,
differential subordination,
weak type inequality,
unconditional constant,
Haar system.

Received by editor(s):
July 8, 2010

Received by editor(s) in revised form:
February 21, 2011

Published electronically:
November 8, 2011

Additional Notes:
Partially supported by MNiSW Grant N N201 397437.

Communicated by:
Richard C. Bradley

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.