Square area integral estimates for subharmonic functions in NTA domains

Shiying Zhao Department of Mathematics and Computer Science, University of Missouri-St. Louis

TBD mathscidoc:1701.332779

Arkiv for Matematik, 30, (1), 345-365, 1991.4
In this paper, we prove a good-λ inequality between the nontangential maximal function and the square area integral of a subharmonic function$u$in a bounded NTA domain$D$in$R$^{$n$}. We achieve this by showing that a weighted Riesz measure of$u$is a Carleson measure, with the Carleson norm bounded by a constant independent of$u$. As consequences of the good-λ inequality, we obtain McConnell-Uchiyama's inequality and an analogue of Murai-Uchiyama's inequality for subharmonic functions in$D$.
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@inproceedings{shiying1991square,
  title={Square area integral estimates for subharmonic functions in NTA domains},
  author={Shiying Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203538907721588},
  booktitle={Arkiv for Matematik},
  volume={30},
  number={1},
  pages={345-365},
  year={1991},
}
Shiying Zhao. Square area integral estimates for subharmonic functions in NTA domains. 1991. Vol. 30. In Arkiv for Matematik. pp.345-365. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203538907721588.
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