Composition Operators on $\bf H^{p,q,s}(B_{n})$ of $\bf \mathbb{C}^{n}$

H. Chen; X. Zhang

Composition Operators on $\bf H^{p,q,s}(B_{n})$ of $\bf \mathbb{C}^{n}$

Complex Variables 2025-05-14 v1

Authors: H. Chen , X. Zhang

Abstract

Let $B_{n}$ be the unit ball in the complex vector space $\mathbb{C}^{n}$ , and let $\varphi: B_{n}\rightarrow B_{n}$ be a holomorphic mapping. In this paper, we characterize those symbols $\varphi$ such that composition operators $C_{\varphi}$ are bounded or compact on the general Hardy type space $H^{p,q,s}(B_{n})$ . These results extend the relevant results on Hardy space and some other classical function spaces.

Keywords

composition operators Hardy spaces holomorphic mappings bounded operators compact operators

Cite

@article{arxiv.2505.08661,
  title  = {Composition Operators on $\bf H^{p,q,s}(B_{n})$ of $\bf \mathbb{C}^{n}$},
  author = {H. Chen and X. Zhang},
  journal= {arXiv preprint arXiv:2505.08661},
  year   = {2025}
}