带有infra-正则核的Teodorescu算子的性质  

Properties of Teodorescu Operators with Inframonogenic Kernel

作　　者：贾珊珊 王丽萍[1] 罗利萍 邱芬 JIA Shanshan;WANG Liping;LUO Liping;QIU Fen(School of Mathematical Sciences,Hebei Normal University,Hebei Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,河北石家庄050024

出　　处：《河北师范大学学报（自然科学版）》2021年第5期433-439,共7页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11401162,11571089,11871191);河北省自然科学基金(A2020205008,A2015205012);河北师范大学重点基金(L2021201)。

摘　　要：正则函数是Clifford分析中重要的研究对象,infra-正则函数是正则函数的推广,也是一类重要函数,因此研究infra-正则函数具有一定的意义.对于正则函数的Teodorescu算子理论的研究已经相对比较成熟,但对于带有infra-正则核的Teodorescu算子的研究相对较少.综合复分析和Clifford分析中的方法研究了带有infra-正则核的Teodorescu算子的性质,包括它的有界性、连续性和可微性等.Teodorescu算子是非齐次偏微分方程边值问题解的核心构件,因此研究带有infra-正则核的Teodorescu算子的性质是非常有必要的.Regular function is an important research object in Clifford analysis,inframonogenic func-tion is a generalization of regular function.It is also a kind of important function.Therefore,the study of inframonogenic function has a certain significance.The theoretical research on Teodorescu operators of regular function has been relatively perfect,but there are few researches on Teodorescu operator with in-framonogenic kernel.In this paper,we study the properties of Teodorescu operator with inframonogenic kernel by combining the method of complex analysis and Clifford analysis,including its boundedness,continuity and differentiability.Teodorescu operator is the core component of the solution to the boundary value problem of nonhomogeneous partial differential equations.So it is necessary to study the properties of Teodorescu operator with inframonogenic kernel.

关 键 词：CLIFFORD分析 infra-正则核 Teodorescu算子 有界性 连续性 可微性 

分 类 号：O177.4[理学—数学]