Hardy spaces of generalized analytic functions and composition operators

• Main Author: Pozzi Elodie
• Format: Article
• Language: English
• Published: De Gruyter 2018-04-01
• Series: Concrete Operators
• Subjects: hardy spaces; generalized analyticity; composition operators; 30h10; 47b33; 30c62
• Online Access: https://doi.org/10.1515/conop-2018-0002

We present some recent results on Hardy spaces of generalized analytic functions on D specifying their link with the analytic Hardy spaces. Their definition can be extended to more general domains Ω . We discuss the way to extend such definitions to more general domains that depends on the regularity of the boundary of the domain ∂Ω. The generalization over general domains leads to the study of the invertibility of composition operators between Hardy spaces of generalized analytic functions; at the end of the paper, we discuss invertibility and Fredholm property of the composition operator C∅ on Hardy spaces of generalized analytic functions on a simply connected Dini-smooth domain for an analytic symbol ∅.