Multipliers of Dirichlet subspaces of the Bloch space

For $0<p<\mathrm{\infty }$ we let ${\mathcal{D}}_{p-1}^p$ denote the space of those functions $f$ which are analytic in the unit disc $\mathbb{D}$ and satisfy ${\int }_{\mathbb{D}}(1-\mathrm{\mid }z\mathrm{\mid })\text{sp}p-1\mathrm{\mid }{f}^{\mathrm{\prime }}(z)\mathrm{\mid }\text{sp}pdA(z)<\mathrm{\infty }$. It is known that, whenever $p\mathrm{\ne }q$, the only multiplier from ${\mathcal{D}}_{p-1}^p$ to ${\mathcal{D}}_{q-1}^q$ is the trivial one. However, if $X$ is a subspace of the Bloch space and $0<p\le q<\mathrm{\infty }$, then $X \cap \mathcal D^p_{p-1}\subset X\cap \mathcal D^q_{q-1} $,afactwhichimpliesthatthespaceofmultipliers$\M(\mathcal D^p_{p-1}\cap X, \mathcal D^q_{q-1} \cap X)$ is non-trivial. In this paper we study the spaces of multipliers $\M(\mathcal D^p_{p-1}\cap X, v\cap X)$($0<p,q<\infty $)fordistinctclassicalsubspaces$X$ of the Bloch space. Specifically, we shall take $X$ to be $H^{\mathrm{\infty }}$, $BMOA$ and the Bloch space $\mathcal{B}$.