On a classification of plane domains for Hardy classes

Kobayashi, Shōji

doi:10.1090/S0002-9939-1978-0486533-9

On a classification of plane domains for Hardy classes
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by Shōji Kobayashi

Proc. Amer. Math. Soc. 68 (1978), 79-82

DOI: https://doi.org/10.1090/S0002-9939-1978-0486533-9

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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 $p \geqslant 1$.

References

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Dennis A. Hejhal, Classification theory for Hardy classes of analytic functions, Bull. Amer. Math. Soc. 77 (1971), 767–771. MR 281907, DOI 10.1090/S0002-9904-1971-12801-X

Classification theory for Hardy classes of analytic functions

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