Weighted theory of Toeplitz operators on the Fock spaces
Abstract
Abstract We study the weighted compactness and boundedness of Toeplitz operators on the Fock spaces. Fix $\alpha>0$ . Let $T_{\varphi }$ be the Toeplitz operator on the Fock space $F^2_{\alpha }$ over $\mathbb {C}^n$ with symbol $\varphi \in L^{\infty }$ . For $1 and any finite sum T of finite products of Toeplitz operators $T_{\varphi }$ ’s, we show that T is compact on the weighted Fock space $F^p_{\alpha ,w}$ if and only if its Berezin transform vanishes at infinity, where w is a restricted $A_p$ -weight on $\mathbb {C}^n$ . Concerning boundedness, for $1\leq p
Fields of Study & Subjects
Holomorphic and Operator Theory
Advanced Harmonic Analysis Research
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Canadian Journal of Mathematics
- Publisher
- Canadian Mathematical Society
- Pages
- 1–26
- Publication date
- 25 March 2026
- Language
- EN