The purpose of this paper is to solve a kind of Riemann–Hilbert problem for \(\Psi \)-hyperholomorphic functions, which are linked with the use of non-standard orthogonal basis of the Euclidean space \({\mathbb R}^m\). We approach this problem using the language of Clifford analysis for obtaining the explicit solution of the problem in a Jordan domain \(\Omega \subset {\mathbb R}^m\). Since our study is concerned with either a smooth or fractal boundary, the data of the problem involve Lipschitz class \({\text{ Lip }}(k-1+\alpha ,\Gamma )\).

中文翻译：

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关于$$\Psi $$ -$${\mathbb R}^m$$ 中的超全纯函数的黎曼-希尔伯特问题

本文的目的是解决\(\Psi \) -超全纯函数的黎曼-希尔伯特问题，该问题与欧几里德空间\({\mathbb R}^的非标准正交基的使用相关联米\）。我们使用 Clifford 分析语言来解决这个问题，以获得 Jordan 域\(\Omega \subset {\mathbb R}^m\)中问题的显式解。由于我们的研究涉及平滑边界或分形边界，因此问题的数据涉及 Lipschitz 类\({\text{ Lip }}(k-1+\alpha ,\Gamma )\)。