Multipliers of Dirichlet-type subspaces of Bloch space
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 429-441
Published online November 8, 2019
Printed March 31, 2020
Songxiao Li, Zengjian Lou, Conghui Shen
Shantou University; Shantou University; Shantou University
Abstract : Let $M(X,Y)$ denote the space of multipliers from $X$ to $Y,$ where $X$ and $Y$ are analytic function spaces. As we known, for Dirichlet-type spaces $\mathcal{D}_{\alpha}^p,$ $M(\mathcal{D}^p_{p-1},\mathcal{D}^q_{q-1})=\{0\},$ if $p\neq q,$ $01,$ then $M(\mathcal{D}^p_{p-2+s},\mathcal{D}^q_{q-2+s})=\{0\}.$ However, $X\cap\mathcal{D}^p_{p-1} \subseteq X\cap\mathcal{D}^q_{q-1}$ and $X\cap \mathcal{D}^p_{p-2+s} \subseteq X\cap \mathcal{D}^q_{q-2+s}$ whenever $X$ is a subspace of the Bloch space $\mathcal{B}$ and $0
Keywords : Multipliers, Carleson measure, Dirichlet-type space, Bloch space
MSC numbers : Primary 30H30, 47B38, 32A37
Supported by : The research was supported by the National Natural Science Foundation of China (Nos.11571217, 11720101003, 11871293) and Key Projects of Fundamental Research in Universities of Guangdong Province (No.2018KZDXM034).
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