Radial limits of $M$-subharmonic functions
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- by David Ullrich PDF
- Trans. Amer. Math. Soc. 292 (1985), 501-518 Request permission
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.References
- J. A. Cima and C. S. Stanton, Admissible limits of $M$-subharmonic functions, Michigan Math. J. 32 (1985), no.Β 2, 211β220. MR 783575, DOI 10.1307/mmj/1029003188
- L. L. Helms, Introduction to potential theory, Pure and Applied Mathematics, Vol. XXII, Wiley-Interscience [A division of John Wiley & Sons, Inc.], 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 $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594, DOI 10.1007/978-1-4613-8098-6
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 292 (1985), 501-518
- MSC: Primary 31B25; Secondary 32A40
- DOI: https://doi.org/10.1090/S0002-9947-1985-0808734-8
- MathSciNet review: 808734