Abstract.
In this paper we deal with the maximal subspace in BMOA where a general semigroup of analytic functions on the unit disk generates a strongly continuous semigroup of composition operators. Particular cases of this question are related to a well-known theorem of Sarason about VMOA. Our results describe analytically that maximal subspace and provide a condition which is sufficient for the maximal subspace to be exactly VMOA. A related necessary condition is also proved in the case when the semigroup has an inner Denjoy-Wolff point. As a byproduct we provide a generalization of the theorem of Sarason.
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This research has been partially supported by the Ministerio de Educación y Ciencia projects n. MTM2006-14449-C02-01 and MTM2005-08350-C03-03 and by La Consejería de Educación y Ciencia de la Junta de Andalucía.
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Blasco, O., Contreras, M.D., Díaz-Madrigal, S. et al. Semigroups of Composition Operators in BMOA and the Extension of a Theorem of Sarason. Integr. equ. oper. theory 61, 45–62 (2008). https://doi.org/10.1007/s00020-008-1568-7
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DOI: https://doi.org/10.1007/s00020-008-1568-7