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On the square function associated with generalized Bochner-Riesz means (1510.05199v2)

Published 18 Oct 2015 in math.CA

Abstract: 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 $L4$ estimate for the associated square function, which we use to derive multiplier theorems for multipliers of the form $m\circ\rho$ where $m:\mathbb{R}\to\mathbb{C}$.

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