On some properties of one Cauchy–Fantappiè integral operator

Close to the Bochner–Martinelli representation is the Cauchy–Fantappié integral representation considered in the paper. The aim of the work is to study the properties of this integral representation for holomorphic functions. The kernel of this integral representation consists of derivatives of the fundamental solution of the Laplace equation. Namely, we consider an integral (integral operator) with this kernel for smooth functions $f$ on the boundary of a bounded domain $D$ with a smooth connected boundary $\Gamma$. The permutation properties of these integral operators are considered.