Solving the Kerzman’s problem on the sup-norm estimate for ∂̄ 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 n -dimensional complex space. The problem has been open since 1971. He also extends and solves the problem on product domains Ω n Ω ^n , where Ω Ω is any bounded domain in C C with C 1 , α C1,α boundary for some α > 0 α >0 .