Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 415, Issue 2, Pages 713-735Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2014.02.005
Keywords
Composition operators; Compact operators; Weakly compact operators; Banach-Saks type theorems; Hyperbolic derivative; Banach spaces of analytic functions; Conformally invariant spaces
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Funding
- MINECO, Spain [MTM2012-37436-C02-01, MTM2012-37436-C02-02]
- FEDER (European Regional Development Fund)
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We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that includes the classical spaces like BMOA, Q(alpha), and analytic Besov spaces B-p. In particular, by combining techniques from both complex and functional analysis, we prove that in this setting weak compactness is equivalent to compactness. For the operators into the corresponding small spaces we also characterize the boundedness and show that it is equivalent to compactness. (C) 2014 Elsevier Inc. All rights reserved.
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