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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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  • J. A. Cima and C. S. Stanton, Admissible limits of $M$-subharmonic functions, Michigan Math. J. 32 (1985), no. 2, 211–220. MR 783575, DOI
  • 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
  • J. E. Littlewood, On functions subharmonic in a circle. III, Proc. London Math. Soc. (2) 32 (1931), 222-234.
  • Walter Rudin, Function theory in the unit ball of ${\bf C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594

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Article copyright: © Copyright 1985 American Mathematical Society