Abstract
We define Hardy classes of bicomplex-valued functions on the complex unit disk which solve bicomplex versions of the Beltrami and related equations. Using representations in terms of their complex-valued counterparts, we show these bicomplex-valued functions recover the boundary behavior associated with the classic holomorphic Hardy spaces. This work generalizes known results for complex-valued functions and continues recent work in the setting of bicomplex analogues of Hardy spaces of both holomorphic and generalized analytic functions. Also, we show Schwarz and Dirichlet boundary value problems associated with the bicomplex Beltrami equation are solvable and provide solution formulas.
Description
This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
Publisher
Springer
Date of publication
7-2025
Language
english
Persistent identifier
http://hdl.handle.net/10950/5149
Document Type
Article
Recommended Citation
Blair, William L., "Bicomplex Hardy Classes of Solutions to Beltrami Equations and the Schwarz Boundary Value Problem" (2025). Math Faculty Publications and Presentations. Paper 2.
http://hdl.handle.net/10950/5149