Properties of Solutions of a Class of Hypocomplex Vector Fields

TL;DR

This paper investigates a Cauchy type integral operator linked to a class of complex coefficient vector fields, demonstrating its properties to establish solution regularity and a strong similarity principle for related equations.

Contribution

It introduces a new integral operator framework for hypocomplex vector fields and proves key properties leading to solvability and similarity principles.

Findings

Holder solvability of semilinear equations is established.

A strong similarity principle for the vector fields is proven.

Properties of the integral operator are characterized.

Abstract

A Cauchy type integral operator is associated to a class of integrable vector fields with complex coefficients. Properties of the integral operator are used to deduce Holder solvability of semilinear equations and a strong similarity principle is established.