Sharp estimates in Bergman and Besov spaces on bounded symmetric domains (Q1862908)

Let \(\Omega\) be a bounded symmetric domain in \(\mathbb{C}^n\). For each parameter \(\alpha>-1\) the authors compare some probability measure \(d v_\alpha\) on \(\Omega\) and consider the corresponding weight Bergman space \(L^p_\alpha (\Omega,dv_\alpha)\), \(0<p<\infty\) in \(\Omega\) of holomorphic functions. They obtain a sharp estimate for the point-evaluation functional on \(L^p_\alpha (\Omega,dv_\alpha)\) (Theorem 1.1). As an application of this theorem they establish a sharp estimate for the derivatives in Besov spaces (Theorem 1.3).