On the \(\Pi\)-operator in Clifford analysis

DOI10.1016/j.jmaa.2015.09.038zbMath1345.30071OpenAlexW2206335040WikidataQ58038850 ScholiaQ58038850MaRDI QIDQ891384

Alí Guzmán Adán, Juan Bory-Reyes, Ricardo Abreu-Blaya, Uwe Kaehler

Publication date: 17 November 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.09.038

zbMATH Keywords

Clifford analysisBeltrami equation\(\Pi\)-operatorTeodorescu transform

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35)

Related Items (12)

On \((\phi,\psi)\)-inframonogenic functions in Clifford analysis ⋮ Spherical \(\Pi \)-type operators in Clifford analysis and applications ⋮ On a Riemann-Hilbert boundary value problem for \((\varphi,\psi)\)-harmonic functions in \(\mathbb{R}^m\) ⋮ On a Riemann-Hilbert problem for \(\Psi\)-hyperholomorphic functions in \(\mathbb{R}^m\) ⋮ Iterated generalized Dirac operators of mixed sides ⋮ Variational integral and some inequalities of a class of quasilinear elliptic system ⋮ Singular integral operators and a \(\overline{\partial}\)-problem for \((\varphi, \psi)\)-harmonic functions ⋮ On the \(\phi \)-hyperderivative of the \(\psi \)-Cauchy-type integral in Clifford analysis ⋮ Reconstruction of solutions to a generalized Moisil-Teodorescu system in Jordan domains with rectifiable boundary ⋮ Higher order Borel-Pompeiu representations in Clifford analysis ⋮ Isomorphisms of partial differential equations in Clifford analysis ⋮ On a generalized Lamé-Navier system in \(\mathbb{R}^3\)

Cites Work

• On the Bergmann kernel function in hyperholomorphic analysis
• An analytic Radon-Nikodym property related to systems of vector-valued conjugate harmonic functions and Clifford analysis
• Extremal inequalities in Sobolev spaces and quasiconformal mappings
• On a spatial generalization of the complex \(\Pi\)-operator
• Subordination by conformal martingales in \(L^{p}\) and zeros of Laguerre polynomials
• On the \(\Pi\)-operator in hyperholomorphic function theory
• Quaternionic Beltrami equations with \(VMO\) coefficients
• Fourier multipliers and Dirac operators
• On some structural sets and a quaternionic (φ,ψ)-hyperholomorphic function theory
• New estimates for the Beurling-Ahlfors operator on differential forms
• A quaternionic Beltrami-type equation and the existence of local homeomorphic solutions
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