The derivative of the atomic function is not in 𝐵^{2/3}

Belna, Charles L.; Muckenhoupt, Benjamin

doi:10.1090/S0002-9939-1977-0586555-2

The derivative of the atomic function is not in $B^{2/3}$
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by Charles L. Belna and Benjamin Muckenhoupt

Proc. Amer. Math. Soc. 63 (1977), 129-130

DOI: https://doi.org/10.1090/S0002-9939-1977-0586555-2

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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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