Absolutely summing Carleson embeddings on weighted Fock spaces with A∞-type weights
Abstract
In this paper, we investigate the r-summing Carleson embeddings on weighted Fock spaces Fpα,w. By using duality arguments, translating techniques and block diagonal operator skills, we completely characterize the r-summability of the natural embeddings Id:Fpα,w→Lpα(μ) for any r⩾1 and p>1, where w is a weight on the complex plane \C that satisfies an Ap-type condition. As applications, we establish some results on the r-summability of differentiation and integration operators, Volterra-type operators and composition operators. Especially, we completely characterize the boundedness of Volterra-type operators and composition operators on vector-valued Fock spaces for all p∈(0,∞), which were left open before for the case p∈(1,2).
Fields of Study & Subjects
Holomorphic and Operator Theory
Approximation Theory and Sequence Spaces
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Journal of Operator Theory
- Publisher
- Theta Foundation
- Volume
- 95
- Issue
- 1
- Pages
- 119–151
- Publication date
- 1 March 2026