The Bloch space and the dual space of a Luecking-type subspace of $A^1$

Abstract

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, Peláez, Pérez-González and Rättyä in 2008, we answer the two questions in the negative.

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