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Proceedings of the American Mathematical Society

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A note on a lemma of Zó

Author: R. Fefferman
Journal: Proc. Amer. Math. Soc. 96 (1986), 241-246
MSC: Primary 42B20; Secondary 42B25
MathSciNet review: 818452
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Abstract: In this article we prove that a general class of singular integrals on product spaces maps $ L\log L$ boundedly to weak $ {L^1}$. We use this to prove a theorem about maximal functions which generalize the strong maximal function.

References [Enhancements On Off] (What's this?)

  • [1] Felipe Zo, A note on approximation of the identity, Studia Math. 55 (1976), no. 2, 111–122. MR 0423013
  • [2] A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85–139. MR 0052553
  • [3] Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
  • [4] Jean-Lin Journé, Calderón-Zygmund operators on product spaces, Rev. Mat. Iberoamericana 1 (1985), no. 3, 55–91. MR 836284, 10.4171/RMI/15
  • [5] R. Fefferman, Calderón-Zygmund theory for product domains-$ {H^p}$ spaces, Proc. Nat. Acad. Sci. U.S.A. (to appear).

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Keywords: Maximal operators, $ L\log L$, singular integrals
Article copyright: © Copyright 1986 American Mathematical Society