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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Removable singularities for $ n$-harmonic functions and Hardy classes in polydiscs


Author: David Singman
Journal: Proc. Amer. Math. Soc. 90 (1984), 299-302
MSC: Primary 32D20; Secondary 32A35
MathSciNet review: 727254
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Abstract: Let $ \phi $ be any strongly convex function. For an open subset $ G$ of a polydisc $ {U^n}$ the Hardy class $ {H_\phi }\left( G \right)$ is the set of analytic functions $ f$ on $ G$ for which $ \phi \circ \log \left\vert f \right\vert$ has an $ n$-harmonic majorant. It is shown that $ {H_\phi }\left( {{U^n} \setminus E} \right) = {H_\phi }\left( {{U^n}} \right)$ for any relatively closed $ n$-negligible subset $ E$ of $ {U^n}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0727254-7
PII: S 0002-9939(1984)0727254-7
Keywords: Polydisc, $ n$-superharmonic function, $ {H_\phi }$ class, Brelot space, $ n$-negligible set
Article copyright: © Copyright 1984 American Mathematical Society