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