We study composition operators on a class of bounded domains including convex domains Ω ⊂ Cn. We show that a general self-map ϕ of Ω always induces a bounded operator Cϕ:Aαp(Ω)→Aα+n-1p(Ω) and the weight gain n- 1 is optimal in certain sense. When ϕ is smooth, we provide explicit examples which reveal aspects quite different from the strongly pseudoconvex domain setting.
Bibliographical notePublisher Copyright:
© 2016, Springer International Publishing.
- Composition operator
- Convex domain
- Finite type domain
- Smooth symbol
ASJC Scopus subject areas
- Algebra and Number Theory