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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Radial limits of $ M$-subharmonic functions


Author: David Ullrich
Journal: Trans. Amer. Math. Soc. 292 (1985), 501-518
MSC: Primary 31B25; Secondary 32A40
MathSciNet review: 808734
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Abstract: "$ M$-subharmonic" functions are defined in the unit ball of $ {{\mathbf{C}}^n}$. Their basic properties are developed, leading to the following generalization of a theorem of Littlewood: An $ M$-subharmonic function such that its restrictions to spheres centered at the origin are bounded in $ {L^1}$ must have radial limits almost everywhere on the unit sphere.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0808734-8
PII: S 0002-9947(1985)0808734-8
Article copyright: © Copyright 1985 American Mathematical Society