On some properties of analytic spaces connected with Bergman metric ball (Q1016766)

Let \(\mu\) be a positive Borel measure on \(B\), \(0<p, q<\infty\) and \(s>-1\). Fix an \(r\in(0, \infty)\) and a sampling sequence \(\{a_k\}_{k\in\mathbb{N}}\). The space \(A(p, q, d\mu)\) consists of all holomorphic functions \(f\) such that \[ \|f\|_{A(p, q, d\mu)}^q=\sum\limits_{k=1}^\infty\left(\int_{D(a_k, r)}|f(z)|^pd\mu(z)\right)^\frac{q}{p}<\infty, \] where \(D(a_k, r)\) is a Bergman metric ball with center \(a_k\) and radius \(r\). In this paper, the authors give some sharp results for these spaces similar to those of Cima and Wogen.