Year: 2019
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Chen, Liwei, McNeal, Jeffery D.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2938598165