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

Stefanie Petermichl; Brett D. Wick

doi:10.1007/s11512-007-0050-0

paper

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

arXiv:math/0701852 · doi:10.1007/s11512-007-0050-0

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.

11 pages, to appear in Arkiv for Matematik

Cited by in corpus (1)

Bilinear forms on weighted Besov spaces