Singular integrals along 𝑁 directions in ℝ²-Reference-Cited by-同舟云学术

Singular integrals along 𝑁 directions in ℝ²

Published:2010-06-11 Issue:12 Volume:138 Page:4433-4442
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Demeter Ciprian

Abstract

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

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2010-138-12/S0002-9939-2010-10442-2/S0002-9939-2010-10442-2.pdf

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