Some properties of k-hypergenic functions in Clifford analysis

Abstract

First, three important theorems related to Clifford Möbius transformations in the real Clifford are given. Then it is proved that the composition of a k-hypergenic function with a Clifford Möbius transformation leads to a k-hypergenic function with weight, where . Finally, the relationships between k-hypergenic functions and -hypergenic functions are obtained, where .

Keywords:

• k-hypergenic function
• Möbius transformation
• real Clifford analysis

AMS Subject Classifications:

• 30B30
• 31B10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Science Foundation of China [grant number 11301136]; [grant number 11571089]; [grant number 11401159]; [grant number 11401162], the Science Foundation of Hebei Province [grant number A2014205069]; [grant number A2014208158]; [grant number A2015205012], the Foundation of Zhejiang Province [grant number LY14A010017] and the Doctoral Foundation of Hebei Normal University [grant numbers L2015B04, L2015B03].