A weighted estimate for the square function on the unit ball in ℂn

Abstract

We show that the Luzin area integral or the square function on the unit ball of ℂⁿ, regarded as an operator in the weighted space L²(w) has a linear bound in terms of the invariant A₂ characteristic of the weight. We show a dimension-free estimate for the “area-integral” associated with the weighted L²(w) norm of the square function. We prove the equivalence of the classical and the invariant A₂ classes.