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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Integrability of superharmonic functions, uniform domains, and Hölder domains


Author: Yasuhiro Gotoh
Journal: Proc. Amer. Math. Soc. 127 (1999), 1443-1451
MSC (1991): Primary 46E15
Published electronically: January 29, 1999
MathSciNet review: 1476132
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Abstract: Let $S^+(D)$ denote the space of all positive superharmonic functions on a domain $D \subset \mathbf R^n$. Lindqvist showed that $\log S^+(D)$ is a bounded subset of $BMO(D)$. Using this, we give a characterization of finitely connected $2$-dimensional uniform domains and remarks on Hölder domains.


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Additional Information

Yasuhiro Gotoh
Email: gotoh@cc.nda.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04670-5
PII: S 0002-9939(99)04670-5
Keywords: BMO, quasihyperbolic metric, uniform domain, H\"older domain, superharmonic function, harmonic function
Received by editor(s): May 7, 1997
Received by editor(s) in revised form: August 25, 1997
Published electronically: January 29, 1999
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1999 American Mathematical Society