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