Solving the Kerzman's problem on the sup-norm estimate for $\bar\partial$ on product domains

Abstract

In this paper, the author solves the long term open problem of Kerzman on sup-norm estimate for Cauchy-Riemann equation on polydisc in $n$-dimensional complex space. The problem has been open since 1971. He also extends and solves the problem on a bounded product domain $\Omega^n$, where $\Omega$ is any bounded domain in $\mathbb{C}$ with $C^{1,\alpha}$ boundary for some $\alpha>0$.