Composition semigroups on BMOA and H∞

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

Anderson, Austin¹  Jovovic, Mirjana¹  Smith, Wayne¹ 

[1] Univ Hawaii, Dept Math, Honolulu, HI 96822 USA

关键词: Composition semigroups;    BMOA;    H-infinity;   

DOI  :  10.1016/j.jmaa.2016.12.032

来源: Elsevier

【 摘 要 】

We study [phi(t), X], the maximal space of strong continuity for a semigroup of composition operators induced by a semigroup {phi(t)}(t >= 0) of analytic self-maps of the unit disk, when X is BMOA, H-infinity or the disk algebra. In particular, we show that [phi(t), BMOA] not equal BMOA for all nontrivial semigroups. We also prove, for every semigroup {phi(t)}(t >= 0), that lim(t -> 0)+ phi(t)(z) = z not just pointwise, but in H-infinity norm. This provides a unified proof of known results about [phi(t), X] when X is an element of {H-P, A(P), B-0, VMOA}. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free