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<p>In this work, we study solutions of Vekua-type generalizations of the polyanalytic equation. We show that Bergman spaces of these functions recover many aspects of the function theory of Bergman spaces of solutions to the Vekua equation. In particular, we prove the existence of a Hodge decomposition in the Hilbert space case. Also, for second-order equations, we show that the real or imaginary part of a solution can be recovered from the imaginary or real part, respectively, and give sufficient conditions for solvability of the associated Dirichlet boundary value problem.</p>

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Generalizations of poly-Bergman spaces and the Bitsadze equation

  • 期刊论文

  • 发表日期：

    2025年10月8日

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  • Briceyda B. Delgado,
  • William L. Blair

摘要

In this work, we study solutions of Vekua-type generalizations of the polyanalytic equation. We show that Bergman spaces of these functions recover many aspects of the function theory of Bergman spaces of solutions to the Vekua equation. In particular, we prove the existence of a Hodge decomposition in the Hilbert space case. Also, for second-order equations, we show that the real or imaginary part of a solution can be recovered from the imaginary or real part, respectively, and give sufficient conditions for solvability of the associated Dirichlet boundary value problem.