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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Martingale transforms and complex uniform convexity
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by J. Bourgain and W. J. Davis PDF
Trans. Amer. Math. Soc. 294 (1986), 501-515 Request permission

Abstract:

Martingale transforms and Calderon-Zygmund singular integral operators are bounded as operators from ${L_2}({L_1})$ to ${L_2}({L_q})$ when $0 < q < 1$. If $Y$ is a reflexive subspace of ${L_1}$ then ${L_1}/Y$ can be renormed to be $2$-complex uniformly convex. A new proof of the cotype 2 property of ${L_1}/{H_1}$ is given.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 501-515
  • MSC: Primary 46E40; Secondary 42B20, 46B99, 60G46
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0825718-5
  • MathSciNet review: 825718