Let \({\mathcal {H}}\) be an oriented three-dimensional manifold and \({\mathbb {H}}_+={\mathbb {R}}_+\oplus {\mathcal {H}}\). The author introduces non-abelian vector valued Fourier transforms on \({\mathcal {H}}\) and Poisson integrals on \({\mathbb {H}}_+\). Through the boundary behaviour of Poisson integral, the author obtains the characterization of conjugate harmonic functions of Fueter type via Riesz transforms.

中文翻译：

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共轭费特型谐波函数

令\（{\ mathcal {H}} \）为定向三维流形，而\（{\ mathbb {H}} _ + = {\ mathbb {R}} _ + \ oplus {\ mathcal {H}} \）。作者介绍了\（{\ mathcal {H}} \）上的非阿贝尔向量值傅立叶变换和\（{\ mathbb {H}} _ + \）上的泊松积分。通过泊松积分的边界行为，作者通过Riesz变换获得了Fueter型共轭谐波函数的刻画。