Some properties of a kind of higher order singular Teodorescu operator in Rⁿ

Abstract

First, the boundedness and Hölder continuous for a kind of higher order singular Teodorescu operators in R ⁿ are discussed. Then the stability and error estimate of the higher order singular Teodorescu operators are given when the boundary surface of integral domain perturbs. Lastly we give an application of the higher order singular Teodorescu operators.

Keywords:

• higher order singular Teodorescu operators
• boundedness
• Hölder continuous
• stability
• perturbation

AMS Subject Classifications:

• 30E20
• 30E25
• 45E05

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 10801043), Natural Science Foundation of Hebei Province (No. A2010000346) and foundation of Hebei University of Science and Technology (No. QD201028).