On Conic Fourier Multipliers

Abstract

We prove a weighted inequality which controls conic Fourier multiplier operators in terms of lacunary directional maximal operators. By bounding the maximal operators, this enables us to conclude that the multiplier operators are bounded on $L^p({\mathbb{R}}^3)$ with $1<p<\infty$.

arXiv comment11 pages, estimates made more precise and references added