Radial $A_p$ weights with applications to the disc multiplier and the Bochner-Riesz operators

Abstract

A characterization of radial A p weights is given in terms of the weights in A p (0, +∞). Together with a result of Mockenhaupt this allows to describe a large class of radial weights for the disc multiplier in terms of the A 2 class of Muckenhoupt. The class of weights is large enough so as to deduce mixed norm inequalities with weights in the radial direction using extrapolation. Similar results are obtained for the Bochner-Riesz operators and for the Littlewood-Paley square function built on characteristic functions of dyadic annuli.