Product domains, MultiCauchy transforms, and the $\bar \partial$ equation
Abstract
Solution operators for the equation $\bar \partial u=f$ are constructed on general product domains in $\mathbb{C}^n$. When the factors are onedimensional, 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.09401
 Bibcode:
 2019arXiv190409401C
 Keywords:

 Mathematics  Complex Variables;
 32W05;
 32A26
 EPrint:
 31 pages