For C¹-functions f, given in the complex space Cn, integral representations of the form f = P(f) - T(∂f) are obtained. Here, P is the orthogonal projector of the space L²{Cn; e-σ|z|ρ |z|γdm(z)} onto its subspace of entire functions and the integral operator T appears by means of explicitly constructed kernel Φ which is investigated in detail.