Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2020; 57(2): 429-441

Online first article November 8, 2019      Printed March 31, 2020

https://doi.org/10.4134/BKMS.b190302

Copyright © The Korean Mathematical Society.

Multipliers of Dirichlet-type subspaces of Bloch space

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).