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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The $\textrm {T}1$ theorem for martingales
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by Andrew G. Bennett PDF
Proc. Amer. Math. Soc. 107 (1989), 493-502 Request permission

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.
References
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • 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