Cauchy transform and rectifiability in Clifford analysis

DOI10.4171/ZAA/1235zbMath1077.30045OpenAlexW2022207359MaRDI QIDQ558475

Ricardo Abreu-Blaya, Juan Bory-Reyes

Publication date: 6 July 2005

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/1235

zbMATH Keywords

Cauchy transformClifford analysisrectifiability

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Functions of hypercomplex variables and generalized variables (30G35) Boundary value problems in the complex plane (30E25) Integral equations with kernels of Cauchy type (45E05)

Related Items (12)

Geometric BVPs, Hardy spaces, and the Cauchy integral and transform on regions with corners ⋮ On the solvability of the jump problem in Clifford analysis ⋮ Jump problem and removable singularities for monogenic functions ⋮ A note on the Bochner-Martinelli integral ⋮ Non-central limit theorems for functionals of random fields on hypersurfaces ⋮ Generalized Moisil-Théodoresco systems and Cauchy integral decompositions ⋮ Cauchy transform on nonrectifiable surfaces in Clifford analysis ⋮ Clifford analysis versus its quaternionic counterparts ⋮ Hölder norm estimate for the Hilbert transform in Clifford analysis ⋮ An Extension Theorem for Biregular Functions in Clifford Analysis ⋮ Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces ⋮ Weighted Cauchy transforms in Clifford analysis

Cites Work

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• Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces
• Singular integrals, analytic capacity and rectifiability
• Harmonic multivector fields and the Cauchy integral decomposition in Clifford analysis
• Clifford Cauchy type integrals on Ahlfors-David regular surfaces in \(\mathbb R^{m+1}\)
• Opérateurs d'intégrale singulière sur les surfaces régulières
• Hausdorff Two-Dimensional Measure in 3-Space
• Convolution Singular Integrals on Lipschitz Surfaces
• Hausdorff m Regular and Rectifiable Sets in n-Space

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