Abstract
In this paper the Théodoresco transform is used to show that, under additional assumptions, each Hölder continuous function f defined on the boundary Γ of a fractal domain Ω ⊂ ℝ2n can be expressed as f = Ψ+ − Ψ−, where Ψ± are Hölder continuous functions on Γ and Hermitian monogenically extendable to Ω and to ℝ2n ∖ (Ω ∪ Γ) respectively.
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Blaya, R.A., Reyes, J.B. & García, T.M. Hermitian decomposition of continuous functions on a fractal surface. Bull Braz Math Soc, New Series 40, 107–115 (2009). https://doi.org/10.1007/s00574-009-0006-z
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DOI: https://doi.org/10.1007/s00574-009-0006-z