A Weighted Estimate for the Square Function on the Unit Ball in $\C^n$

Details A Weighted Estimate for the Square Function on the Unit Ball in $\C^n$ A Weighted Estimate for the Square Function on the Unit Ball in $\C^n$

2007-01-29

arxiv.org/abs/math/0701852v1

Ark. Mat. 45 (2007), no. 2, 337--350

Mathematics

Complex Variables

11 pages, to appear in Arkiv for Matematik

Scientific paper

10.1007/s11512-007-0050-0

We show that the Lusin area integral or the square function on the unit ball of $\C^n$, regarded as an operator in weighted space $L^2(w)$ has a linear bound in terms of the invariant $A_2$ characteristic of the weight. We show a dimension-free estimate for the ``area-integral'' associated to the weighted $L^2(w)$ norm of the square function. We prove the equivalence of the classical and the invariant $A_2$ classes.

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