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Proceedings of the American Mathematical Society

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

 

 

On the restricted mean value property


Author: P. C. Fenton
Journal: Proc. Amer. Math. Soc. 100 (1987), 477-481
MSC: Primary 31A05
DOI: https://doi.org/10.1090/S0002-9939-1987-0891149-1
MathSciNet review: 891149
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Abstract: Suppose that $ u$ is continuous in the open unit disc and has the restricted mean value property. It is shown that if $ u$ has finite boundary limits almost everywhere, and if $ u$ possesses a harmonic majorant and minorant, the difference between which has finite radial upper limits everywhere, then $ u$ is harmonic.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0891149-1
Article copyright: © Copyright 1987 American Mathematical Society