  Let $X$ be the dual space of a Luecking-type subspace of the Bergman space
$A^1$. It is known that the Bloch space $\mathcal{B}$ is a subset of $X$. In
1990, Ghatage and Sun asked whether $\mathcal{B}$ is dense in $X$. They also
asked whether the little version of $X$ is a subset of $\mathcal{B}$. In this
note, based on results and methods of Girela, Pel\'aez, P\'erez-Gonz\'alez and
R\"atty\"a in 2008, we answer the two questions in the negative.
