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- W4287083640 abstract "We study the weighted compactness and boundedness properties of Toeplitz operators on the Bergman space with respect to B'ekoll`e-Bonami type weights. Let $T_u$ denote the Toeplitz operator on the (unweighted) Bergman space of the unit ball in $mathbb{C}^n$ with symbol $u in L^{infty}$. We characterize the compact Toeplitz operators on the weighted Bergman space $mathcal{A}^p_sigma$ for all $sigma$ in a subclass of the B'ekoll`e-Bonami class $B_p$ that includes radial weights and powers of the Jacobian of biholomorphic mappings. Concerning boundedness, we show that $T_u$ extends boundedly on $L^p_{sigma}$ for $p in (1,infty)$ and weights $sigma$ in a $u$-adapted class of weights containing $B_p$, and we establish analogous weighted endpoint weak-type $(1,1)$ bounds for weights beyond $B_1$." @default.
- W4287083640 created "2022-07-25" @default.
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- W4287083640 date "2021-07-07" @default.
- W4287083640 modified "2023-10-03" @default.
- W4287083640 title "Weighted theory of Toeplitz operators on the Bergman space" @default.
- W4287083640 doi "https://doi.org/10.48550/arxiv.2107.03457" @default.
- W4287083640 hasPublicationYear "2021" @default.
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