There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions. In this paper, we present an equivalent characterization for the boundedness of the product operator C_ϕD^m acting on Bloch-type spaces of slice regular functions. After that, an equivalent estimation for its essential norm is established, which can imply several existing results on holomorphic spaces.

中文翻译：

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切片正则函数的Bloch型空间之间的乘积算子

关于作用于四元数上定义的切片正则函数空间的四元数算子的性质的工作很少。在本文中，我们提出了作用在切片正则函数的 Bloch 型空间上的乘积算子C _ϕ D ^m的有界性的等效表征。之后，建立其本质范数的等效估计，这可以暗示全纯空间上的几个现有结果。