Laurent Expansion and L2-Boundary Values in Hermitian Clifford Analysis

Inspired by the classical Cauchy transform in L 2 ( ∂ B ( R ) ) , we first derive the Laurent expansion for Hermitian monogenic functions in Hermitian Clifford analysis, and we obtain direct applications of this expansion. Then we use the Laurent expansion to study the L 2 -boundary values of Hermit...

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Bibliographic Details
Published in:Complex analysis and operator theory 2024, Vol.18 (7)
Main Authors: He, Fuli, Huang, Song
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Online Access:Get full text
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Summary:Inspired by the classical Cauchy transform in L 2 ( ∂ B ( R ) ) , we first derive the Laurent expansion for Hermitian monogenic functions in Hermitian Clifford analysis, and we obtain direct applications of this expansion. Then we use the Laurent expansion to study the L 2 -boundary values of Hermitian monogenic functions, we prove that every f ∈ L 2 ( S 2 m - 1 ; V ) can be decomposed as a sum of boundary values of functions, which are h -monogenic inside and outside the unit ball respectively.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-024-01609-y