Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The derivative of the atomic function is not in $ B\sp{2/3}$


Authors: Charles L. Belna and Benjamin Muckenhoupt
Journal: Proc. Amer. Math. Soc. 63 (1977), 129-130
MSC: Primary 30A78
MathSciNet review: 0586555
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Abstract: H. A. Allen and C. L. Belna have shown that the derivative of the atomic function $ A(z) = \exp [(z + 1)/(z - 1)]$ is in $ {B^p}$ for $ 0 < p < 2/3$, where $ {B^p}$ is the containing Banach space for the Hardy class $ {H^p}(0 < p < 1)$. Here we show that $ A'(z)$ does not belong to any of the other $ {B^p}$ spaces.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0586555-2
Article copyright: © Copyright 1977 American Mathematical Society