Some integral properties in Clifford analysis

Abstract

Two kinds of integral properties in Clifford analysis are considered. The first deals with the boundary properties of the Cauchy singular integral when the boundary is composed of piecewise smooth surfaces. The second discusses the connections between the weighted integral operators and the orthogonal polynomials. Both are closely connected with the Borel–Pompeiu formula.

Keywords:

• Clifford analysis; Borel–Pompeiu formula; Orthogonal polynomials

AMS Subject Classification::

• 30C60

Acknowledgements

The author appreciates the help of Professor Jianke Lu and Professor Jinyuan Du. The project was supported by National Natural Science Foundation of China (No. 10471107) and SF of Wuhan University (No. 20127004).