Semigroups of composition operators and integral operators in spaces of analytic functions

By Ó. Blasco, Manuel D. Contreras, S. Díaz-Madrigal, Josep Martínez, M. Papadimitrakis, A. Siskakis. 2013

53 citations recorded by the source corpus.

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 V MOA 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/56525300c63f529ee28d112a06fb264736d22766

Citations in the corpus

• Integral operators mapping into the space of bounded analytic functions (2016, unknown): “ons [28], in order to show that the g ∈ H∞ such that lim δ→0+ kg − gδkH∞ = 0, belong to A, where gδ(z) = g(eiδz), for any δ ∈ R. A proof of this result can be obtained using ideas on semigroup theory [6]. Namely, if g(z) = −iz then Tg : H∞ → A is bounded, so if one considers the semigroup {ϕt(z) = e”