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
n
-dimensional complex space. The problem has been open since 1971. He also extends and solves the problem on product domains
Ω
n
\Omega ^n
, where
Ω
\Omega
is any bounded domain in
C
\mathbb {C}
with
C
1
,
α
C^{1,\alpha }
boundary for some
α
>
0
\alpha >0
.