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

Stefanie Petermichl·Brett D. Wick
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Abstract

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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Stefanie Petermichl, Brett D. Wick. 2007-01-29. A Weighted Estimate for the Square Function on the Unit Ball in $\C^n$. https://doi.org/10.1007/s11512-007-0050-0

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