This paper aims to study the jump problem for monogenic functions in fractal hypersurfaces of Euclidean spaces. The notion of the Marcinkiewicz exponent has been taken into consideration. A new solvability condition is obtained, basing the work on specific properties of the Teodorescu transform in Clifford analysis. It is shown that this condition improves those involving the Minkowski dimension.

中文翻译：

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$${\mathbb {R}}^{n+1}$$ 分形域中的 Marcinkiewicz 指数和边值问题

本文旨在研究欧几里得空间分形超曲面中单基因函数的跳跃问题。Marcinkiewicz 指数的概念已被考虑在内。基于 Clifford 分析中 Teodorescu 变换的特定性质，获得了新的可解性条件。结果表明，该条件改善了涉及 Minkowski 维数的条件。