Teodorescu transform for slice monogenic functions and applications

Chao Ding; Zhenghua Xu

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arXiv · 2402.01997

Teodorescu transform for slice monogenic functions and applications

Chao Ding·Zhenghua Xu

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Abstract

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.

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BibTeX RIS

Chao Ding, Zhenghua Xu. 2025-01-10. Teodorescu transform for slice monogenic functions and applications. https://arxiv.org/abs/2402.01997

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