Solving the Kerzman’s problem on the sup-norm estimate for \overline{∂} 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 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 .