A kind of Riemann and Hilbert boundary value problem for left monogenic functions in R^m (m ≥ 2)

Abstract

In this article, some properties of Cauchy-type integral and singular integral with integration domain

are discussed, especially their boundary value properties at ∞. With the help of Painlevé theorem and Liouville theorem, a Riemann Boundary Value Problem (BVP for short) and a Hilbert BVP for left monogenic functions in Clifford analysis are investigated in the classical sense, their explicit representation of solutions are obtained respectively.

Keywords:

• Cauchy-type integral
• Singular integral
• Riemann BVP
• Hilbert BVP
• Monogenic function
• MS(2000) Subject Classification: 30G35

Acknowledgment

Yafang Gong wishes to show his sincere thanks to the referee whose opinions greatly improved the results of this article and the same gratitude to Prof. Tao Qian (Macau University) with whom he held useful discussions on the results of Section 2. This project was supported by SF of Wuhan University.

Notes

†E-mail: [email protected]

Additional information

Notes on contributors

Jinyuan Du †

†E-mail: [email protected]