Abstract
For a positive integer k ≥ 2, the kth-order slant weighted Toeplitz operator \({U_{k,\phi}^{\beta}}\) on \({L^{2}(\beta)}\) with \({\phi \in L^{\infty}(\beta)}\) is defined as \({U_{k,\phi}^{\beta}=W_{k}M_{\phi}^{\beta}}\), where \({W_{k}e_{n}(z)=\frac{\beta_{m}}{\beta_{km}}e_m(z)}\) if \({n=km, m\in\mathbb{Z}}\) and \({W_{k}e_n(z)= 0}\) if n ≠ km. The paper derives relations among the symbols of two kth-order slant weighted Toeplitz operators so that their product is a kth-order slant weighted Toeplitz operator. We also discuss the compactness and the case for two kth-order slant weighted Toeplitz operators to commute essentially.
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