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We show that the Lusin area integral or the square function on the unit ballof $\C^n$, regarded as an operator in weighted space $L^2(w)$ has a linearbound in terms of the invariant $A_2$ characteristic of the weight. We show adimension-free estimate for the ``area-integral'' associated to the weighted$L^2(w)$ norm of the square function. We prove the equivalence of the classicaland the invariant $A_2$ classes.Comment: 11 pages, to appear in Arkiv for Matemati

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