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ISSN 1088-6826(e) ISSN 0002-9939(p)

Singular integrals along directions in $\mathbb{R}^2$

Author(s): Ciprian Demeter
Journal: Proc. Amer. Math. Soc. 138 (2010), 4433-4442.
MSC (2010): Primary 42B20; Secondary 42B25
Posted: June 11, 2010
MathSciNet review: 2680067
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Abstract | References | Similar articles | Additional information

Abstract: We prove optimal bounds in $L^2(\mathbb{R}^2)$ for the maximal operator obtained by taking a singular integral along arbitrary directions in the plane. We also give a new proof for the optimal bound for the single scale Kakeya maximal function in the plane.

References:

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Additional Information:

Ciprian Demeter
Affiliation: Department of Mathematics, Indiana University, 831 East 3rd Street, Bloomington, Indiana 47405
Email: demeterc@indiana.edu

DOI: 10.1090/S0002-9939-2010-10442-2
PII: S 0002-9939(2010)10442-2
Keywords: Kakeya maximal function, singular integrals
Received by editor(s): January 12, 2010
Received by editor(s) in revised form: February 12, 2010
Posted: 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 of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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