The Riesz transform for the harmonic oscillator in spherical coordinates

Ó. Ciaurri, L. Roncal

Published 2013-04-02, updated 2014-03-27Version 2

In this paper we show weighted estimates in mixed norm spaces for the Riesz transform associated with the harmonic oscillator in spherical coordinates. In order to prove the result we need a weighted inequality for a vector-valued extension of the Riesz transform related to the Laguerre expansions which is of independent interest. The main tools to obtain such extension are a weighted inequality for the Riesz transform independent of the order of the involved Laguerre functions and an appropriate adaptation of Rubio de Francia's extrapolation theorem.