Teodorescu transform for slice monogenic functions and applications
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913643203919872 |
|---|---|
| author | Ding, Chao Xu, Zhenghua |
| author_facet | Ding, Chao Xu, Zhenghua |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01997 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Teodorescu transform for slice monogenic functions and applications Ding, Chao Xu, Zhenghua Complex Variables 30G35, 32A30, 44A05 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. |
| title | Teodorescu transform for slice monogenic functions and applications |
| topic | Complex Variables 30G35, 32A30, 44A05 |
| url | https://arxiv.org/abs/2402.01997 |