Some properties of a T operator with B-M kernel in the complex Clifford analysis

• Main Authors: Zunfeng Li, Yuying Qiao, Nanbin Cao
• Format: Article
• Language: English
• Published: SpringerOpen 2018-08-01
• Series: Journal of Inequalities and Applications
• Subjects: Complex Clifford analysis; Teodorescu operator; Boundedness; Hölder continuity; γ-integrability
• Online Access: http://link.springer.com/article/10.1186/s13660-018-1816-6

Abstract Teodorescu operator, or T-operator, plays an important role in Vekua equation systems and the generalized analytic function theory. It is a generalized solution to the nonhomogeneous Dirac equation. The properties of T operators play a key role in the study of boundary value problems and integral representation of the solutions. In this paper, we first define a Teodorescu operator with B-M kernel in the complex Clifford analysis and prove the boundedness of this operator. Then we give an inequality similar to the classical Hile lemma about real vector which plays a key role in the following proof. Finally, we prove the Hölder continuity and γ-integrability of this operator.