A sharp weak type inequality for martingale transforms and other subordinate martingales

Author:
Jiyeon Suh

Journal:
Trans. Amer. Math. Soc. **357** (2005), 1545-1564

MSC (2000):
Primary 60G44, 60G42; Secondary 60G46

DOI:
https://doi.org/10.1090/S0002-9947-04-03563-9

Published electronically:
September 23, 2004

MathSciNet review:
2115376

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a martingale difference sequence, a sequence of numbers in , and a positive integer, then

Here denotes the best constant. If , then as was shown by Burkholder. We show here that for the case , and that is also the best constant in the analogous inequality for two martingales and indexed by , right continuous with limits from the left, adapted to the same filtration, and such that is nonnegative and nondecreasing in . In Section 7, we prove a similar inequality for harmonic functions.

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Additional Information

**Jiyeon Suh**

Affiliation:
Department of Statistics, Purdue University, West Lafayette, Indiana 47907

Email:
jsuh@stat.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9947-04-03563-9

Keywords:
Martingale transform,
differential subordination,
biconcave majorant

Received by editor(s):
February 19, 2003

Received by editor(s) in revised form:
November 4, 2003

Published electronically:
September 23, 2004

Article copyright:
© Copyright 2004
American Mathematical Society