On the Π-operator in Clifford analysis

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• 作者：Ricardo Abreu Blaya^a ; ^{rabreu@facinf.uho.edu.cu" class="auth_mail" title="E-mail the corresponding author} ; Juan Bory Reyes^b ; ^{juanboryreyes@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Alí ; Guzm&aacute ; n Ad&aacute ; n^c ; ^{ali.guzmanadan@ugent.be" class="auth_mail" title="E-mail the corresponding author} ; Uwe Kä ; hler^d ; ^{ukaehler@ua.pt" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Clifford analysis ; Teodorescu transform ; Pi-operator ; Beltrami equation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：434
• 期：2
• 页码：1138-1159
• 全文大小：494 K

文摘

In this paper we prove that a generalization of complex Π-operator in Clifford analysis, obtained by the use of two orthogonal bases of a Euclidean space, possesses several mapping and invertibility properties, as studied before for quaternion-valued functions as well as in the standard Clifford analysis setting. We improve and generalize most of those previous results in this direction and additionally other consequent results are presented. In particular, the expression of the jump of the generalized Π-operator across the boundary of the domain is obtained as well as an estimate for the norm of the Π-operator is given. At the end an application of the generalized Π-operator to the solution of Beltrami equations is studied where we give conditions for a solution to realize a local and global homeomorphism.