The Bloch space for the minimal ball (Q2773397)

The minimal ball is a non-homogeneous, non-Reinhardt domain in \(\mathbb{C}^{n}\) defined by the inequality \(\sum_{j=1}^{n} |z_{j}|^{2} + |\sum_{j=1}^{n} z_{j}^{2} |<1\). Function theory on the minimal ball has attracted attention recently, especially since Oeljeklaus, Pflug, and Youssfi computed its Bergman kernel function explicitly [\textit{K. Oeljeklaus, P. Pflug}, and \textit{El Hassan Youssfi}, Ann. Inst. Fourier 47, No. 3, 915-928 (1997; Zbl 0873.32025)]. Let \(A^{1}\) denote the space of holomorphic functions on the minimal ball that are absolutely integrable with respect to Lebesgue measure weighted by the factor \(|\sum_{j=1}^{n} z_{j}^{2}|^{-1/2}\). The author proves that the dual space of \(A^{1}\) can be identified with the Bloch space of the minimal ball (which is defined in this context by a radial derivative condition).