Levi foliations in pseudoconvex boundaries and vector fields that commute approximately with $\bar \partial $

Abstract

Boas and Straube proved a general sufficient condition for global regularity of the ∂-Neumann problem in terms of families of vector fields that commute approximately with ∂. In this paper, we study the existence of these vector fields on a compact subset of the boundary whose interior is foliated by complex manifolds. This question turns out to be closely related to properties of interest from the point of view of foliation theory.