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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Boundary limits of subharmonic functions in the disc


Author: M. Stoll
Journal: Proc. Amer. Math. Soc. 93 (1985), 567-568
MSC: Primary 31A20
DOI: https://doi.org/10.1090/S0002-9939-1985-0774024-0
MathSciNet review: 774024
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Abstract: In this note we prove the following: let $f\not \equiv - \infty$ be subharmonic in $\left | z \right | < 1$ satisfying $\lim \limits _{r \to 1} \int _0^{2\pi } {f(r{e^{i\theta }})d\theta = 0}$ with $f(z) \leqslant 0$; then \[ \lim \limits _{r \to 1} \sup (1 - r)\inf \limits _{\left | z \right | = r} f(z) = 0\].


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Article copyright: © Copyright 1985 American Mathematical Society