Open AccessSingular integrals along 𝑁 directions in ℝ²
Author(s) -
Ciprian Demeter
Publication year - 2010
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-2010-10442-2
Subject(s) - algorithm , annotation , artificial intelligence , computer science , mathematics
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.