论文标题
加权构图运算符从$ h^\ infty $到有界均匀域的Bloch空间
Weighted composition operators from $H^\infty$ to the Bloch space of a bounded homogeneous domain
论文作者
论文摘要
令$ d $为$ \ mathbb {c}^n $中的一个有界的均匀域。在本文中，我们研究了有限的和紧凑的加权构图操作员，将hardy空间$ h^\ infty（d）$映射到$ d $的bloch空间中。我们表征了一度加权构图操作员，提供操作员规范估计，并提供足够的紧凑条件。我们证明，对于单位球和多磁性，这些条件是必要的。然后，我们表明，如果$ d $是一个有界的对称域，则有限的乘法运算符，从$ h^\ infty（d）$到$ d $的bloch空间是符号有限的运算符。
Let $D$ be a bounded homogeneous domain in $\mathbb{C}^n$. In this paper, we study the bounded and the compact weighted composition operators mapping the Hardy space $H^\infty(D)$ into the Bloch space of $D$. We characterize the bounded weighted composition operators, provide operator norm estimates, and give sufficient conditions for compactness. We prove that these conditions are necessary in the case of the unit ball and the polydisk. We then show that if $D$ is a bounded symmetric domain, the bounded multiplication operators from $H^\infty(D)$ to the Bloch space of $D$ are the operators whose symbol is bounded.
