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Proceedings of the American Mathematical Society

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

 
 

 

The $\textrm {T}1$ theorem for martingales


Author: Andrew G. Bennett
Journal: Proc. Amer. Math. Soc. 107 (1989), 493-502
MSC: Primary 60G46; Secondary 42B20
DOI: https://doi.org/10.1090/S0002-9939-1989-0979217-9
MathSciNet review: 979217
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Abstract: The $T1$ theorem of David and Journé gives necessary and sufficient conditions that a singular integral operator be bounded from ${L^2}({R^n})$ to ${L^2}({R^n})$. In this paper, the definition of singular integral operator is extended to the setting of operators on ${L^2}(\Omega )$ where $\Omega$ denotes Wiener space. The main theorem is that the $T1$ theorem holds in this new setting.


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Article copyright: © Copyright 1989 American Mathematical Society