Corpus ID: 119676282

Separate regularity and extension theorems for regular functions of several quaternionic variables

@article{Baracco2018SeparateRA,
  title={Separate regularity and extension theorems for regular functions of several quaternionic variables},
  author={L. Baracco and Martino Fassina and S. Pinton},
  journal={arXiv: Complex Variables},
  year={2018}
}
We prove that a function of several quaternionic variables is regular in the sense of Fueter if and only if it is regular in each variable separately, thus providing a quaternionic analog of a celebrated theorem of Hartogs. We also establish a result similar in spirit to the Hanges and Tr\`eves theorem, showing that a disc contained in the boundary of a domain is a propagator of regular extendibility across the boundary. 

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