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Representations of bounded harmonic functions

T. S. Mountford Department of Mathematics, University of California, Los Angeles S. C. Port Department of Mathematics, University of California, Los Angeles

TBD mathscidoc:1701.332745

Arkiv for Matematik, 29, (1), 107-126, 1990.8
An open subset$D$of$R$^{$d$},$d≧2$, is called Poissonian iff every bounded harmonic function on the set is a Poisson integral of a bounded function on its boundary. We show that the intersection of two Poissonian open sets is itself Poissonian and give a sufficient condition for the union of two Poissonian open sets to be Poissonian. Some necessary and sufficient conditions for an open set to be Poissonian are also given. In particular, we give a necessary and sufficient condition for a Greenian$D$to be Poissonian in terms of its Martin boundary.
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@inproceedings{t.1990representations,
  title={Representations of bounded harmonic functions},
  author={T. S. Mountford, and S. C. Port},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203534735278554},
  booktitle={Arkiv for Matematik},
  volume={29},
  number={1},
  pages={107-126},
  year={1990},
}
T. S. Mountford, and S. C. Port. Representations of bounded harmonic functions. 1990. Vol. 29. In Arkiv for Matematik. pp.107-126. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203534735278554.
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