INTEGRAL PRODUCTS, BOCHNER-MARTINELLI TRANSFORMS AND APPLICATIONS

Abstract

A generalized Bochner-Martinelli formula for the push-forward of a Lipschitz function over a weak Stokes domain is proved. By means of integral products, the $\bar \partial$-Euler and the $\bar \partial$-Neumann vector fields, local and global characterizations of the holomorphicity of functions on a Riemann domain are given. As further applications characterizations of isogeneity and Liouville properties for the push-forward of semi-harmonic functions on an analytic covering space are obtained.