Uniform Estimates for the Canonical Solution to the partial derivative--equation on Product Domains

We obtain uniform estimates for the canonical solution to partial derivative<overline>u=f on the Cartesian product of bounded planar domains with C-2 boundaries, when f is continuous up to the boundary. This generalizes Landucci's result for the bidisc toward higher dimensional product domains. In particular, it answers an open question of Kerzman for continuous datum.