Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 67-90
Universidad de Valencia, Departamento de Análisis Matemático
46100 Burjassot, Valencia, Spain; Oscar.Blasco 'at' uv.es
Universidad de Sevilla,
Departamento de Matemática Aplicada II
Camino de los Descubrimientos, s/n, 41092, Sevilla,
Spain; contreras 'at' us.es
Universidad de Sevilla,
Departamento de Matemática Aplicada II
Camino de los Descubrimientos, s/n, 41092, Sevilla,
Spain; madrigal 'at' us.es
Universidad de Valencia, Departamento de Análisis Matemático
46100 Burjassot, Valencia, Spain; Josep.Martinez 'at' uv.es
University of Crete, Department of Mathematics
Knossos Avenue 714 09 Iraklion-Crete, Greece;
papadim 'at' math.uoc.gr
Aristotle University of Thessaloniki, Department of Mathematics
54124 Thessaloniki, Greece; siskakis 'at' math.auth.gr
Abstract. We study the maximal spaces of strong continuity on BMOA and the Bloch space B for semigroups of composition operators. Characterizations are given for the cases when these maximal spaces are VMOA or the little Bloch B0. These characterizations are in terms of the weak compactness of the resolvent function or in terms of a specially chosen symbol g of an integral operator Tg. For the second characterization we prove and use an independent result, namely that the operators Tg are weakly compact on the above mentioned spaces if and only if they are compact.
2010 Mathematics Subject Classification: Primary 30H05, 32A37, 47B33, 47D06; Secondary 46E15.
Key words: Composition semigroups, BMOA, Bloch spaces, integration operators, weak compactness.
Reference to this article: O. Blasco, M.D. Contreras, S. Díaz-Madrigal, J. Martínez, M. Papadimitrakis and A.G. Siskakis: Semigroups of composition operators and integral operators in spaces of analytic functions. Ann. Acad. Sci. Fenn. Math. 38 (2013), 67-90.
doi:10.5186/aasfm.2013.3806
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