Multipliers and closures of Besov-type Spaces in the Bloch space

Abstract

Let $p>1$ and $\rho\geq 0$. A function $f\in H(\D)$ belongs to the space $B_p(\rho)$ (see \cite{CMF}) if
$$
\|f\|_{B_p(\rho)}^p =|f(0)|^p+\int_{\D}
\left|(1-|z|^2)f'(z)\right|^{p}\frac{\rho\left(1-|z|^2\right)}{(1-|z|^2)^2}dA(z)<\infty.
$$
In this paper, motivated by \cite{BG} and \cite{GG}, under some conditions on weighted function $\rho$, we investigated the closures of $B_p(\rho)$ spaces in the Bloch space $C_{\B}(\B\cap B_p(\rho))$. Moreover, we proved that interpolating Blaschke products in $C_{\B}(\B\cap B_p(\rho))$ is multipliers of $B_p(\rho)\cap BMOA$.