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arXiv · 1904.09401

Product domains, Multi-Cauchy transforms, and the $\bar \partial$ equation

Liwei Chen·Jeffery D. McNeal
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Abstract

Solution operators for the equation $\bar \partial u=f$ are constructed on general product domains in $\mathbb{C}^n$. When the factors are one-dimensional, the operator is a simple integral operator: it involves specific derivatives of $f$ integrated against iterated Cauchy kernels. For higher dimensional factors, the solution is constructed by solving sub-$\bar \partial$ equations with modified data on the factors. Estimates of the operators in several norms are proved.

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Liwei Chen, Jeffery D. McNeal. 2019-04-20. Product domains, Multi-Cauchy transforms, and the $\bar \partial$ equation. https://arxiv.org/abs/1904.09401

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