EMIS ELibM Electronic Journals Publications de l’Institut Mathématique, Nouvelle Série
Vol. 100[114], No. 1/1, pp. 1–16 (2016)

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Miroslav Pavlović

Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

Abstract: We consider the space 𝔅 log α 1 , of analytic functions on the unit disk 𝔻, defined by the requirement 𝔻 |f ' (z)|ϕ(|z|)dA(z)<, where ϕ(r)=log α (1/(1-r)) and show that it is a predual of the “log α -Bloch” space and the dual of the corresponding little Bloch space. We prove that a function f(z)= n=0 a n z n with a n 0 is in 𝔅 log α 1 iff n=0 log α (n+2)/(n+1)< and apply this to obtain a criterion for membership of the Libera transform of a function with positive coefficients in 𝔅 log α 1 . Some properties of the Cesàro and the Libera operator are considered as well.

Keywords: Libera operator; Cesaro operator; Hardy spaces; logarithmic Bloch type spaces; predual

Classification (MSC2000): 30D55

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Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.

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