Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 593-609

COMPOSITION OPERATORS ON HARDY–ORLICZ SPACES ON PLANAR DOMAINS

Michal Rzeczkowski

Adam Mickiewicz University, Faculty of Mathematics and Computer Science
61-614 Poznan, Poland; rzeczkow 'at' amu.edu.pl

Abstract. We show isomorphic and isometric characterizations of Hardy–Orlicz spaces on multiply-connected domains whose boundary consists of finitely many disjoint analytic Jordan curves. We also study composition operators on these spaces. In particular we obtain characterization of compact composition operators on Hardy–Orlicz spaces in terms of Carleson's measures defined in the paper.

2010 Mathematics Subject Classification: Primary 47B33, 46E30.

Key words: Hardy–Orlicz spaces, composition operators, Hardy spaces on planar domain, Carleson measures.

Reference to this article: M. Rzeczkowski: Composition operators on Hardy–Orlicz spaces on planar domains. Ann. Acad. Sci. Fenn. Math. 42 (2017), 593-609.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4240