| 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 |
