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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Radial limits of $ n$-subharmonic functions in the polydisc

Authors: W. C. Nestlerode and M. Stoll
Journal: Trans. Amer. Math. Soc. 279 (1983), 691-703
MSC: Primary 32A22; Secondary 42B25
MathSciNet review: 709577
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Abstract: We prove a relation between a certain weighted radial limit of an $ n$-subharmonic function in the polydisc $ {U^n}$ and the representing measure of its least $ n$-harmonic majorant. We apply this result to functions in $ N({U^n})$, the Nevalinna class of $ {U^n}$. In particular, we obtain a necessary condition for a function to belong to the component of the origin in $ N({U^n})$. These results are extensions of the work of J. H. Shapiro and A. L. Shields to $ n > 1$.

References [Enhancements On Off] (What's this?)

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  • [5] Manfred Stoll, The space 𝑁_{∗} of holomorphic functions on bounded symmetric domains, Ann. Polon. Math. 32 (1976), no. 1, 95–110. MR 0417438

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Article copyright: © Copyright 1983 American Mathematical Society