Solving the Kerzman's problem on the sup-norm estimate for $\text{dbar}$ on product domains

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 ${\mathrm{\Omega }}^n$, where $\mathrm{\Omega }$ either is simply connected with $C^{1,\alpha }$ boundary or satisfies a uniform exterior ball condition with piecewise $C^1$ boundary.