Cauchy–Pompeiu representations for higher order elliptic equations in the unit ball

In this paper we consider the Pompeiu operator in the higher dimensional complex unit ball. The explicit form of its iteration is given. The operator is iterated just once leading to some particular solution to an inhomogeneous bianalytic system. We prove the explicit form of this iteration. Moreover, some further properties, e.g., the kernel space, of the Pompeiu operator are discussed, which gives an application to the pluriharmonic differential system.