论文标题
独特的伯格曼空间之间的Toeplitz运营商
Toeplitz operators between distinct Bergman spaces
论文作者
论文摘要
对于$ -1 <α<\ infty $，令$ω_α（z）=（1+α）（1- | z |^2）^α$为单位磁盘的标准重量。在此注释中，我们提供了toeplitz运算符的界限和紧凑性的描述，$ t_ {μ，β} $在不同的加权伯格曼空间之间$ -1 <α，β<\ infty $和$ 0 <p \ leq 1 <q <\ infty，-1 <β\leqα<\ infty $。我们的结果可以看作是\ cite {pau}的Pau和Zhao作品的扩展。此外，即使在未加权的设置中，主要结果的部分是新的。
For $-1<α<\infty$, let $ω_α(z)=(1+α)(1-|z|^2)^α$ be the standard weight on the unit disk. In this note, we provide descriptions of the boundedness and compactness for the Toeplitz operators $T_{μ,β}$ between distinct weighted Bergman spaces $L_{a}^{p}(ω_α)$ and $L_{a}^{q}(ω_β)$ when $0<p\leq1$, $q=1$, $-1<α,β<\infty$ and $0<p\leq 1<q<\infty, -1<β\leqα<\infty$, respectively. Our results can be viewed as extensions of Pau and Zhao's work in \cite{Pau}. Moreover, partial of main results are new even in the unweighted settings.
