Weighted \(\overline{\partial}\)-integral representations of \(C^1\)-functions in \(\mathbb C^n\)
Summary: For \(C^1\)-functions \(f\) given in the complex space \(\mathbb C^n\), integral representations of the form \[ f = P(f) - T(\overline{\partial}f) \] are obtained. Here \(P\) is the orthogonal projector of the space \[ L^2 \Big\{\mathbb C^n; e^{-\sigma|z|^\rho} |z|^\gamma dm(z)\Big\} \] onto its subspace of entire functions, and the integral operator \(T\) is defined by means of an explicitly constructed kernel \(\Phi\), which is investigated in detail.
scientific article; zbMATH DE number 6032353
scientific article