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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Singular integrals along $N$ directions in $\mathbb {R}^2$
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by Ciprian Demeter PDF
Proc. Amer. Math. Soc. 138 (2010), 4433-4442 Request permission

Abstract:

We prove optimal bounds in $L^2(\mathbb {R}^2)$ for the maximal operator obtained by taking a singular integral along $N$ arbitrary directions in the plane. We also give a new proof for the optimal $L^2$ bound for the single scale Kakeya maximal function in the plane.
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Additional Information
  • Ciprian Demeter
  • Affiliation: Department of Mathematics, Indiana University, 831 East 3rd Street, Bloomington, Indiana 47405
  • MR Author ID: 734783
  • Email: demeterc@indiana.edu
  • Received by editor(s): January 12, 2010
  • Received by editor(s) in revised form: February 12, 2010
  • Published electronically: June 11, 2010
  • Additional Notes: The author is supported by a Sloan Research Fellowship and by NSF Grants DMS-0742740 and 0901208
  • Communicated by: Michael T. Lacey
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 4433-4442
  • MSC (2010): Primary 42B20; Secondary 42B25
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10442-2
  • MathSciNet review: 2680067