$$L^p$$Lp-Regularity for $$\\bar{\\partial }$$∂¯ on Products of Unit Balls

Abstract

In this paper, we prove that the $$\\bar{\\partial }$$∂¯-operator has closed range in $$L^p$$Lp-spaces and further the canonical solution of the $$\\bar{\\partial }$$∂¯-problem gains 1/2 derivative in the so-called partial $$L^p$$Lp-Sobolev spaces as well as global boundary regularity for $$\\bar{\\partial }$$∂¯ on products of unit balls.