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Analytic functions of bounded mean oscillation and the Bloch space. (English) Zbl 0796.46011

Summary: We show that the closure of the space BMOA of analytic functions of bounded mean oscillation in the Bloch space \({\mathcal B}\) is the image \(P({\mathcal U})\) of the space of all continuous functions on the maximal ideal space of \(H^ \infty\) under the Bergman projection \(P\). It is proved that the radial growth of functions in \(P({\mathcal U})\) is slower than the iterated logarithm studied by Makarow. So some geometric conditions are given for functions \(P({\mathcal U})\), which we can easily use to construct many Bloch functions not in \(P({\mathcal U})\).

MSC:

46E15 Banach spaces of continuous, differentiable or analytic functions
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
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