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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 in the Nevanlinna class and in the Hardy classes


Author: Juhani Riihentaus
Journal: Proc. Amer. Math. Soc. 102 (1988), 546-550
MSC: Primary 32D20
MathSciNet review: 928977
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Abstract: We show that certain sets in $ {{\mathbf{C}}^n},n \geq 2$, which we call $ n$-small, are removable singularities for holomorphic functions in the Nevanlinna class. Since our class of sets includes polar sets (in $ {{\mathbf{R}}^{2n}}$) our result includes the previous removable singularity results for the Nevanlinna class. We give also a related result for a subclass of the Hardy class.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0928977-0
PII: S 0002-9939(1988)0928977-0
Keywords: Holomorphic function, meromorphic function, removable singularity set, polar set, Hausdorff measure, Riesz mass, harmonic majorant
Article copyright: © Copyright 1988 American Mathematical Society