Arkiv för Matematik

  • Ark. Mat.
  • Volume 29, Number 1-2 (1991), 107-126.

Representations of bounded harmonic functions

T. S. Mountford and S. C. Port

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An open subset D of Rd, 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.


Supported by NSF DMS86-01800.

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Ark. Mat., Volume 29, Number 1-2 (1991), 107-126.

Received: 8 August 1990
First available in Project Euclid: 31 January 2017

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1991 © Institut Mittag-Leffler


Mountford, T. S.; Port, S. C. Representations of bounded harmonic functions. Ark. Mat. 29 (1991), no. 1-2, 107--126. doi:10.1007/BF02384334.

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