%0 Journal Article
%T On the square function associated with generalized Bochner-Riesz means
%A Laura Cladek
%J Mathematics
%D 2015
%I arXiv
%X We consider generalized Bochner-Riesz multipliers of the form $(1-\rho(\xi))_+^{\lambda}$ where $\rho:\mathbb{R}^2\to\mathbb{R}$ belongs to a class of rough distance functions homogeneous with respect to a nonisotropic dilation group. We prove a critical $L^4$ estimate for the associated square function, which we use to derive multiplier theorems for multipliers of the form $m\circ\rho$ where $m:\mathbb{R}\to\mathbb{C}$.
%U http://arxiv.org/abs/1510.05199v2