<ovl>∂</ovl>-problem in domains of ℂ2in terms of hyper-conjugate harmonic functions

DOI10.1080/17476933.2011.598933zbMath1252.30032OpenAlexW2018688230MaRDI QIDQ3167672

Ricardo Abreu-Blaya, Juan Bory-Reyes, Michael V. Shapiro, Maria Elena Luna-Elizarrarás

Publication date: 2 November 2012

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2011.598933

zbMATH Keywords

Cauchy-Fueter operatorBorel-Pompeiu formula\(\overline \partial\)-problemhyper-conjugate harmonic functionsThéodoresco operator

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Holomorphic functions of several complex variables (32A10)

Related Items (4)

A quaternionic treatment of inhomogeneous Cauchy-Riemann type systems in some traditional theories ⋮ Solutions of inhomogeneous generalized Moisil-Teodorescu systems in Euclidean space ⋮ Singular integral operators and a \(\overline{\partial}\)-problem for \((\varphi, \psi)\)-harmonic functions ⋮ Solutions of inhomogeneous perturbed generalized Moisil-Teodorescu system and Maxwell's equations in Euclidean space

Cites Work

• The Gauss-Green theorem for fractal boundaries
• A new characterization of a class of pseudoconvex domains in \(\mathbb C^2\)
• Quaternionic analysis
• Complex Analysis: A Brief Tour into Higher Dimensions
• On conjugate harmonic functions in Euclidean space
• Differentiation of the Martinelli‐Bochner Integrals and the Notion of Hyperderivability
• On the interplay between the Hilbert transform and conjugate harmonic functions

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