Radial limits of -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
DOI:
https://doi.org/10.1090/S0002-9947-1983-0709577-4
MathSciNet review:
709577
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Abstract | References | Similar Articles | Additional Information
Abstract: We prove a relation between a certain weighted radial limit of an -subharmonic function in the polydisc
and the representing measure of its least
-harmonic majorant. We apply this result to functions in
, the Nevalinna class of
. In particular, we obtain a necessary condition for a function to belong to the component of the origin in
. These results are extensions of the work of J. H. Shapiro and A. L. Shields to
.
- [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
and
, J. Reine Angew. Math. 282 (1976), 80-87. MR 0404692 (53:8492)
- [5]
-, The space
of holomorphic functions on bounded symmetric domains, Ann. Polon. Math. 32 (1976), 95-110. MR 0417438 (54:5488)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1983-0709577-4
Article copyright:
© Copyright 1983
American Mathematical Society