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A weighted estimate for the square function on the unit ball in ℂ^{$n$}

Stefanie Petermichl Department of Mathematics, University of Texas at Austin Brett D. Wick Department of Mathematics, Vanderbilt University

TBD mathscidoc:1701.333114

Arkiv for Matematik, 45, (2), 337-350, 2006.8
We show that the Luzin area integral or the square function on the unit ball of ℂ^{$n$}, regarded as an operator in the 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 with 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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@inproceedings{stefanie2006a,
  title={A weighted estimate for the square function on the unit ball in ℂ^{$n$}},
  author={Stefanie Petermichl, and Brett D. Wick},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203620865225923},
  booktitle={Arkiv for Matematik},
  volume={45},
  number={2},
  pages={337-350},
  year={2006},
}
Stefanie Petermichl, and Brett D. Wick. A weighted estimate for the square function on the unit ball in ℂ^{$n$}. 2006. Vol. 45. In Arkiv for Matematik. pp.337-350. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203620865225923.
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