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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 on Hölder domains of the plane


Author: Makoto Masumoto
Journal: Proc. Amer. Math. Soc. 117 (1993), 1083-1088
MSC: Primary 31A05; Secondary 30C20
MathSciNet review: 1152284
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Abstract: We prove that if $ D$ is a finitely connected Hölder domain of the plane, then there exists $ p > 0$ for which every positive superharmonic function on $ D$ is $ p$-integrable over $ D$ with respect to two-dimensional Lebesgue measure.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1152284-9
PII: S 0002-9939(1993)1152284-9
Keywords: Hölder domain, quasi-hyperbolic metric, superharmonic function, harmonic function, conformal mapping
Article copyright: © Copyright 1993 American Mathematical Society