Weighted composition operators from $H^{\infty }$ to the Bloch space of a bounded homogeneous domain

Abstract

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.

References in corpus (1)

• Weighted Composition Operators between different Bloch-type Spaces in Polydisk

Cited by in corpus (1)

• Reproducing kernel Hilbert spaces supporting nontrivial Hermitian weighted composition operators