Teodorescu transform for slice monogenic functions and applications
| Title: | Teodorescu transform for slice monogenic functions and applications |
|---|---|
| Authors: | Ding, Chao, Xu, Zhenghua |
| Publication Year: | 2024 |
| Collection: | Mathematics |
| Subject Terms: | Mathematics - Complex Variables, 30G35, 32A30, 44A05 |
| More Details: | In the past few years, the theory of slice monogenic functions has been developed rapidly mainly motivated by the applications to an elegant functional calculus for non-commuting operators. In this article, we introduce the Teodorescu transform in the theory of slice monogenic functions, which turns out to be the right inverse of a slice Cauchy-Riemann operator. The boundednesses of the Teodorescu transform and its derivatives are investigated as well. A Hodge decomposition of the $\mathcal{L}^p$ space and a generalized Bergman projection are introduced at the end as applications. Comment: 27 pages |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2402.01997 |
| Accession Number: | edsarx.2402.01997 |
| Database: | arXiv |
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