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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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  • [CS] J. A. Cima and C. S. Stanton, Admissible limits of 𝑀-subharmonic functions, Michigan Math. J. 32 (1985), no. 2, 211–220. MR 783575, 10.1307/mmj/1029003188
  • [HE] L. L. Helms, Introduction to potential theory, Pure and Applied Mathematics, Vol. XXII, Wiley-Interscience A Division of John Wiley & Sons, New York-London-Sydney, 1969. MR 0261018
  • [LW] J. E. Littlewood, On functions subharmonic in a circle. III, Proc. London Math. Soc. (2) 32 (1931), 222-234.
  • [RU] Walter Rudin, Function theory in the unit ball of 𝐶ⁿ, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594

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DOI: https://doi.org/10.1090/S0002-9947-1985-0808734-8
Article copyright: © Copyright 1985 American Mathematical Society