自守复合算子的本质正规性
Essential Normality of automorphic composition operators
摘要：
首先刻画了加权Bergman空间$A^2_s(D)$上对任意实$s>-1$本质正规的复合算子，其中诱导符号是单位圆盘$D$的自同构.利用同样的技巧，我们研究了Hardy空间$H^2(B_N)$和加权Bergman空间$A^2_s(B_N)$（$s>-1$）上的自守复合算子.进一步，我们给出了单位球$B_N$的线性分式自映射诱导的非本质正规的复合算子。
英文摘要：
We first characterize those composition operators that are essentially normal on the weighted Bergman space $A^2_s(D)$ for any real $s>-1$, where induced symbols are automorphisms of the unit disk $D$. Using the same technique, we investigate the automorphic composition operators on the Hardy space $H^2(B_N)$ and the weighted Bergman spaces $A^2_s(B_N)$ ($s>-1$). Furthermore, we give some composition operators induced by linear fractional self-maps of the unit ball $B_N$ that are not essentially normal.
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