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A Cauchy Transform for Polymonogenic Functions on Fractal Domains

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Abstract

A Cauchy integral representation formula for polymonogenic functions has been established in smoothly bounded domains, but the method by which it has been obtained cannot be extended to the case of domains with fractal boundary. In this paper an alternative polymonogenic Cauchy transform is defined, which enables us to obtain several types of integral representation formulae, including the Cauchy and Borel-Pompeiu representations in this very general geometric setting.

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Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

We thank the two anonymous reviewers whose comments, answers and suggestions helped improve and clarify this manuscript.

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Authors and Affiliations

  1. Unidad Académica de Matemáticas, Universidad Autónoma de Guerrero, Ave. Lázaro Cárdenas, 39087, Chilpancingo, Guerrero, México

    Tania Rosa Gómez Santiesteban, Ricardo Abreu Blaya, Juan C. Hernández Gómez & José María Sigarreta Almira

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  1. Tania Rosa Gómez Santiesteban
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  2. Ricardo Abreu Blaya
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  3. Juan C. Hernández Gómez
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  4. José María Sigarreta Almira
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Communicated by Roman Lavicka.

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This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

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Santiesteban, T.R.G., Blaya, R.A., Gómez, J.C.H. et al. A Cauchy Transform for Polymonogenic Functions on Fractal Domains. Complex Anal. Oper. Theory 16, 42 (2022). https://doi.org/10.1007/s11785-022-01228-5

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