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Teodorescu transform for slice monogenic functions and applications (2402.01997v3)
Published 3 Feb 2024 in math.CV
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.