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July 28, 2026Journal of Geometric AnalysisOpen Access

Bicomplex Hardy Classes of Solutions to Beltrami Equations and the Schwarz Boundary Value Problem

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Authors

WBWilliam L. Blair

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Overview

Randomized trial explores boundary behavior of bicomplex solutions in Hardy classes, suggesting broader applications for general analytic functions.

Key Points

  • This work aims to define Hardy classes for bicomplex-valued functions that solve bicomplex Beltrami equations and examine their boundary behavior.
  • Defined bicomplex Hardy classes on the complex unit disk.
  • Used complex-valued representations to analyze the bicomplex functions.
  • Established solvability of the Schwarz and Dirichlet boundary value problems.
  • Bicomplex-valued functions exhibit boundary behavior similar to classic holomorphic Hardy spaces.
  • Schwarz boundary value problems associated with bicomplex Beltrami equations are solvable.
  • Provided explicit solution formulas for boundary value problems.

Cite This Study

William L. Blair (2026) studied this question.

synapsesocial.com/papers/6a6850eb2845b684d16eff31https://doi.org/10.1007/s12220-026-02537-3
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