Some properties of a T operator with B-m kernel in the complex Clifford analysis. (English) Zbl 07445942

Summary: 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 \(\gamma\)-integrability of this operator.


30G35 Functions of hypercomplex variables and generalized variables
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
32A30 Other generalizations of function theory of one complex variable
30A05 Monogenic and polygenic functions of one complex variable
47B91 Operators on complex function spaces
15A66 Clifford algebras, spinors
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