Bergman theory for the inhomogeneous Cimmino system

TL;DR

This paper extends Bergman theory to inhomogeneous Cimmino systems using quaternionic analysis, establishing integral theorems and exploring applications in weighted Bergman spaces and conformal invariance.

Contribution

It introduces a quaternionic analysis approach to inhomogeneous Cimmino systems, deriving integral formulas and analyzing their applications in Bergman spaces.

Findings

Proved Cauchy's integral theorem for inhomogeneous Cimmino systems.

Derived Cauchy type formulas in quaternionic analysis.

Explored applications to weighted Bergman spaces and conformal invariants.

Abstract

We first prove a Cauchy's integral theorem and Cauchy type formula for certain inhomogeneous Cimmino system from quaternionic analysis perspective. The second part of the paper directs the attention towards some applications of the mentioned results, dealing in particular with four kinds of weighted Bergman spaces, reproducing kernels, projection and conformal invariant properties.