Bicomplex Hardy Classes of Solutions to Higher-Order Vekua Equations
arXiv:2505.04593 · doi:10.1016/j.jmaa.2023.127690
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.
Changes from last version: 1. Many typographical and notational errors were corrected. 2. The definition of the integral operator in Theorem 2.17 was corrected. 3. Aspects of the referenced background material have been condensed and/or clarified. Other minor improvements throughout. The results of all new theorems are unchanged outside of corrections necessary due to typographical errors