Illinois Journal of Mathematics

A class of Möbius invariant function spaces

Kehe Zhu

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Abstract

We introduce a class of Möbius invariant spaces of analytic functions in the unit disk, characterize these spaces in terms of Carleson type measures, and obtain a necessary and sufficient condition for a lacunary series to be in such a space. Special cases of this class include the Bloch space, the diagonal Besov spaces, BMOA, and the so-called $Q_p$ spaces that have attracted much attention lately.

Article information

Source
Illinois J. Math., Volume 51, Number 3 (2007), 977-1002.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258131114

Digital Object Identifier
doi:10.1215/ijm/1258131114

Mathematical Reviews number (MathSciNet)
MR2379734

Zentralblatt MATH identifier
1154.30040

Subjects
Primary: 30H05: Bounded analytic functions
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions

Citation

Zhu, Kehe. A class of Möbius invariant function spaces. Illinois J. Math. 51 (2007), no. 3, 977--1002. doi:10.1215/ijm/1258131114. https://projecteuclid.org/euclid.ijm/1258131114


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