On compactness and Lp‐regularity in the ∂¯‐Neumann problem

Abstract

Let Ω be a C 4 -smooth bounded pseudoconvex domain in C 2 . We show that if the ∂ ¯ -Neumann operator N 1 is compact on L ( 0 , 1 ) 2 ( Ω ) , then the embedding operator J : D o m ( ∂ ¯ ) ∩ D o m ( ∂ ¯ ∗ ) → L ( 0 , 1 ) 2 ( Ω ) is L p -regular for all 2 ⩽ p < ∞ .