Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

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


Author: Ciprian Demeter
Journal: Proc. Amer. Math. Soc. 138 (2010), 4433-4442
MSC (2010): Primary 42B20; Secondary 42B25
Published electronically: June 11, 2010
MathSciNet review: 2680067
Full-text PDF

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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 42B20, 42B25

Retrieve articles in all journals with MSC (2010): 42B20, 42B25


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10442-2
Keywords: Kakeya maximal function, singular integrals
Received by editor(s): January 12, 2010
Received by editor(s) in revised form: February 12, 2010
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.