Boundedness of Multiparameter Forelli-Rudin Type Operators on Product Lᵖ Spaces over Tubular Domains

In this paper, we introduce and study two classes of multiparameter Forelli-Rudin type operators from L^p (TB TB, dV䃑 dV䃒) to L^q (TB TB, dV䃑 dV䃒), especially on their boundedness, where L^p (TB TB, dV䃑 dV䃒) and L^q (TB TB, dV䃑 dV䃒) are both weighted Lebesgue spaces over the Cartesian product of two tubular domains TB TB, with mixed-norm and appropriate weights. We completely characterize the boundedness of these two operators when 1 p q<. Moreover, we provide the necessary and sufficient condition of the case that q= (, ). As an application, we obtain the boundedness of three common classes of integral operators, including the weighted multiparameter Bergman-type projection and the weighted multiparameter Berezin-type transform.