On the dual space of a weighted Bergman space on the unit ball of \({\mathbb{C}}^ n\) (Q1115993)

Let \(B_ n\) denote the unit ball in \({\mathbb{C}}^ n\), \(n\geq 2\), with boundary S. For \(0<p<\infty\) and \(\alpha \geq -1,\) the weighted Bergman space \(A^ p_{\alpha}\) consists of all holomorphic functions on \(B_ n\) for which \[ \| f\|^ p_{p,\alpha} = \begin{cases} \int^{1}_{0} M^ p_ p (r;f) (1-r)^{\alpha} 2nr^{2n-1} dr < \infty, \quad&\alpha >-1 \\ \sup_{0\leq r<1} M^ p_ p (r;f) < \infty, \quad&\text{for }\alpha =-1 \end{cases} \] where \(M^ p_ p(r,t)=\int_{S}| f(rt)|^ pd\sigma (t)\). In the paper the author computes the dual space of the space \(A^ p_{\alpha}(B_ n)\) for \(0<p<1\) by determining the Mackey topology of \(A^ p_{\alpha}\).