Forelli-Rudin type theorem in pluriharmonic Bergman spaces with small index (Q1974178)

Let \(H(B)\) (resp. \(h(B)\)) be the space of all holomorphic (resp. pluriharmonic) functions on the unit ball \(B\) in \(\mathbb{C}^n\). After recalling the notion of the Bergman type operator \(T_s\) \((s\in\mathbb{R})\) on the Lebesgue space \(L^p(B)\), the authors prove that, for \(0< p< 1\), \(T_s\) is a bounded projection from \(L^p(B)\cap H(B)\) onto \(L^p(B)\cap H(B)\) for \(s> (p^{-1}- 1)(n+ 1)\). As an application, the authors show that the Gleason's problem is solvable in the Bergman space \(L^p(B)\cap H(B)\) for \(0< p< 1\).