Some properties of the Teodorescu operator related to the α-Dirac operator

Abstract

In this paper, we first define Teodorescu operator related to the -Dirac operator in Clifford analysis. Then we discuss the existence, q-times integrability, differentiability and mapping properties of Teodorescu operator in a nonempty open set , which is bounded connected.

Keywords:

• Clifford analysis
• α-Dirac operator
• Teodorescu operator
• existence and q-times integrability
• mapping properties

AMS Subject Classifications:

• 30G30
• 32A55

Notes

Dedicated to Professor Wei Lin on the occasion of his 80th birthday.

This work was supported by the National Science Foundation of China [grant number 11301136], [grant number 11171349] and the Natural Science Foundation of Hebei Province [No. A2014208158].