  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.
