Analytic functions with decreasing coefficients and Hardy and Bloch spaces

The following rather surprising result is noted. (1) A function f(z) = ∑anzn such that an ↓ 0 (n → ∞) belongs to H1 if and only if ∑(an/(n + 1)) < ∞. A more subtle analysis is needed to prove that assertion (2) remains true if H1 is replaced by the predual, 1(⊂ H1), of the Bloch space. Assertion...

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Veröffentlicht in:	Proceedings of the Edinburgh Mathematical Society 2013-06, Vol.56 (2), p.623-635
1. Verfasser:	Pavlovic, Miroslav
Format:	Artikel
Sprache:	eng
Schlagworte:	Analytic functions Mathematical analysis Mathematical functions Proof theory Proving Theorems Transforms
Online-Zugang:	Volltext
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