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H. A. Allen and C. L. Belna have shown that the derivative of the atomic function A(z) = exp [(z + \)/(z 1)] is in B" for 0 > (1 r)(\ cos 9) + 2r(l cos 9) 1 1 cos 9 Received by the editors February 7, 1973 and, in revised form, March 9, 1976. A MS (MOS) subject classifications (1970). Primary 30A78. 'Supported in part by NSF grant MPS 75-07596. ©American Mathematical Society 1977

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