Abstract.
A new perspective on a Cauchy integral formula for Clifford algebras valued functions on domains with quite smooth boundaries was discussed in [5]. On the other hand, the Cauchy transform associated to Clifford analysis has been involved recently with fractional metric dimensions and fractals, see [1, 2, 3].
In this paper we consider the question of possible generalizations of the Cauchy integral formula to domains with fractal boundary. As an application, we prove a Martinelli-Bochner type formula for several complex variables on such pathological domains. The proof makes heavy use of the isotonic approach of the monogenic functions theory.
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Received: 8 October 2008
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Abreu-Blaya, R., Bory-Reyes, J. A Martinelli-Bochner formula on fractal domains. Arch. Math. 92, 335–343 (2009). https://doi.org/10.1007/s00013-009-3049-x
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DOI: https://doi.org/10.1007/s00013-009-3049-x