Integrability of superharmonic functions on Hölder domains of the plane

Masumoto, Makoto

doi:10.1090/S0002-9939-1993-1152284-9

Integrability of superharmonic functions on Hölder domains of the plane
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by Makoto Masumoto

Proc. Amer. Math. Soc. 117 (1993), 1083-1088

DOI: https://doi.org/10.1090/S0002-9939-1993-1152284-9

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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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