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PreprintarXiv licencearXiv

Higher order Teodorescu transform in the theory of generalized partial-slice monogenic functions

  • Manjie Hu
  • Chao Ding
Open at sourcePDFDOICite

Abstract

This paper investigates the higher order Teodorescu transform in the context of generalized partial-slice monogenic functions. By introducing the generalized poly-partial-slice Cauchy kernel, we derive some integral formulas including higher order Borel-Pompeiu formula and Cauchy integral formula for generalized poly-partial-slice monogenic functions. Furthermore, we define the higher order Teodorescu transform in this context and establish its existence, continuity, and some mapping properties. These results extend classical integral methods in Clifford analysis to the generalized poly-partial-slice setting.

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Cite

BibTeXRIS
BibTeX
@misc{hu2026higher,
  title = {{Higher order Teodorescu transform in the theory of generalized partial-slice monogenic functions}},
  author = {Manjie Hu and Chao Ding},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39238},
  eprint = {2610.39238},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39238},
}
RIS
TY  - UNPB
TI  - Higher order Teodorescu transform in the theory of generalized partial-slice monogenic functions
AU  - Manjie Hu
AU  - Chao Ding
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39238
UR  - https://arxiv.org/abs/2610.39238
AB  - This paper investigates the higher order Teodorescu transform in the context of generalized partial-slice monogenic functions. By introducing the generalized poly-partial-slice Cauchy kernel, we derive some integral formulas including higher order Borel-Pompeiu formula and Cauchy integral formula for generalized poly-partial-slice monogenic functions. Furthermore, we define the higher order Teodorescu transform in this context and establish its existence, continuity, and some mapping properties. These results extend classical integral methods in Clifford analysis to the generalized poly-partial-slice setting.
ER  -