Three-parameter Triebel–Lizorkin spaces associated with a sum of two flag singular integrals

In this paper, the authors establish the three-parameter Triebel–Lizorkin spaces and characterize these spaces as the intersection of two flag Triebel–Lizorkin spaces by applying the discrete Littlewood–Paley–Stein analysis. Moreover, they obtain the boundedness of product singular integral operators on the three-parameter Triebel–Lizorkin spaces.