Abstract
In this paper we show that the closure of the space BMOA of analytic functions of bounded mean oscillation in the Bloch spaceB is the image P(U) of space of all continuous functions on the maximal ideal space ofH ∞ under the Bergman projection P. It is proved that the radial growth of functions in P(U) is slower than the iterated logarithm studied by Makarov. So some geometric conditions are given for functions in P(U), which we can easily use to construct many Bloch functions not in P(U).
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Ghatage, P.G., Zheng, D. Analytic functions of bounded mean oscillation and the Bloch space. Integr equ oper theory 17, 501–515 (1993). https://doi.org/10.1007/BF01200391
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DOI: https://doi.org/10.1007/BF01200391