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

Abstract

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