论文标题
在一类径向重量引起的加权伯格曼空间上的Toeplitz操作员
Toeplitz operators on weighted Bergman spaces induced by a class of radial weights
论文作者
论文摘要
假设$ω$是单位磁盘上满足前向和反向加倍条件的径向重量。使用Carleson措施和$ T1 $ -TYPE条件，我们获得了正骨量的必要条件$μ$，以使Toeplitz操作员$ t_ {μ，ω}：l^p_a（ω）\ to l_a^1（ω）$的限制，并以$ 0 <p \ p \ p \ leq 1 $ $ 0 <p \ p \ p \ leq leq leq 1 $。此外，我们在$ l^1_a（ω）$上的$ l^1（ω）$符号的有限toeplitz运算符获得了凸起条件。这概括了\ cite {Zhu1989}中Zhu的结果。
Suppose that $ω$ is a radial weight on the unit disk that satisfies both forward and reverse doubling conditions. Using Carleson measures and $T1$-type conditions, we obtain necessary and sufficient conditions of the positive Borel measure $μ$ such that the Toeplitz operator $T_{μ,ω}:L^p_a(ω)\to L_a^1(ω)$ is bounded and compact for $0<p\leq 1$. In addition, we obtain a bump condition for the bounded Toeplitz operators with $L^1(ω)$ symbol on $L^1_a(ω)$. This generalizes a result of Zhu in \cite{zhu1989}.
