Weighted ∂¯-Integral Representations of C1-Functions in C n

Abstract EN

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.