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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?)

  • [1] J. W. Roberts, The component of the origin in the Nevanlinna class, Illinois J. Math. 19 (1975), 553-559. MR 0382672 (52:3554)
  • [2] W. Rudin, Function theory in polydiscs, Benjamin, New York, 1969. MR 0255841 (41:501)
  • [3] J. H. Shapiro and A. L. Shields, Unusual topological properties of the Nevanlinna class, Amer. J. Math. 97 (1976), 915-936. MR 0390227 (52:11053)
  • [4] M. Stoll, Harmonic majorants for plurisubharmonic functions on bounded symmetric domains with applications to the spaces $ {H_\Phi }$ and $ {N_{\ast}}$, J. Reine Angew. Math. 282 (1976), 80-87. MR 0404692 (53:8492)
  • [5] -, The space $ {N_{\ast}}$ of holomorphic functions on bounded symmetric domains, Ann. Polon. Math. 32 (1976), 95-110. MR 0417438 (54:5488)

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Article copyright: © Copyright 1983 American Mathematical Society

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