Sobolev regularity of the canonical solutions to ∂ ¯ on product domains

Abstract

Let Ω be a product domain in C n , n ≥ 2, where each slice has smooth boundary. We observe that the canonical solution operator for the ∂ equation on Ω is bounded in W k,p (Ω), k ∈ Z + , 1 < p < ∞. This Sobolev regularity is sharp in view of Kerzman-type examples.