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Conjugate Harmonic Functions of Fueter Type

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Abstract

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.

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Acknowledgements

The author would like to express his deep thanks to the referees for their very careful reading and useful comments which do improve the presentation of this article. This work was partially supported by the Natural Science Foundation of Xinjiang Urgur Autonomous Region (Grants Nos. 2019D01C049, 62008031 and 042312023).

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  1. College of Mathematics and Information Sciences, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Xingya Fan

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  1. Xingya Fan
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Correspondence to Xingya Fan.

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Communicated by Wolfgang Sprössig

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This work was partially supported by the Natural Science Foundation of Xinjiang Urgur Autonomous Region (Grants Nos. 2019D01C049, 62008031 and 042312023).

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Fan, X. Conjugate Harmonic Functions of Fueter Type. Adv. Appl. Clifford Algebras 30, 32 (2020). https://doi.org/10.1007/s00006-020-01057-9

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