Bicomplex Hardy Classes of Solutions to Higher-Order Vekua Equations

TL;DR

This paper extends representation formulas for Hardy class solutions to higher-order Vekua equations into the bicomplex setting, demonstrating boundary value properties of these solutions.

Contribution

It introduces bicomplex Hardy classes for higher-order Vekua equations and establishes their boundary value characteristics, advancing the theory of bicomplex analysis.

Findings

Representation formulas for bicomplex Hardy class solutions

Existence of nontangential boundary values

Boundary values in the sense of distributions

Abstract

We extend representation formulas for functions in Hardy classes of solutions to higher-order iterated Vekua equations to Hardy classes of bicomplex-valued functions that solve a bicomplex version of the Vekua equation or its higher-order generalizations. Using these representations, we show that functions in these bicomplex-valued Hardy classes have nontangential boundary values and boundary values in the sense of distributions.