Composition Operators on Generalized Hardy Spaces

Juliette Leblond (1) , Elodie Pozzi (2) , Emmanuel Russ (3)

1 APICS - Analysis and Problems of Inverse type in Control and Signal processing
2 IMB - Institut de Mathématiques de Bordeaux
3 IF - Institut Fourier

We study the composition operators f↦f∘ϕ on generalized analytic function spaces named generalized Hardy spaces, on bounded domains of C, for holomorphic functions ϕ with uniformly bounded derivative. In particular, we provide necessary and/or sufficient conditions on ϕ, depending on the geometry of the domains, ensuring that these operators are bounded, invertible, or isometric.

Mots clés: Generalized Hardy spaces; Composition operators

Domaines: Mathématiques [math]

Juliette Leblond, Elodie Pozzi, Emmanuel Russ. Composition Operators on Generalized Hardy Spaces. Complex Analysis and Operator Theory, 2015, ⟨10.1007/s11785-015-0464-9⟩. ⟨hal-01242032v1⟩