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

 

On a classification of plane domains for Hardy classes


Author: Shōji Kobayashi
Journal: Proc. Amer. Math. Soc. 68 (1978), 79-82
MSC: Primary 30A78
MathSciNet review: 0486533
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Abstract: For every positive nubmer p, let $ {O_p}$ denote the class of plane domains W for which the Hardy class $ {H_p}(W)$ contains no nonconstant functions, and $ O_p^ - = \cup \{ {O_q}:0 < q < p\} $. In this paper it is proved that $ {O_p}$ strictly contains $ O_p^ -$ if $ p \geqslant 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0486533-9
PII: S 0002-9939(1978)0486533-9
Keywords: Hardy class, harmonic majorant, subharmonic function, superharmonic function
Article copyright: © Copyright 1978 American Mathematical Society