  Boas and Straube proved a general sufficient condition for global regularity
of the d-bar Neumann problem in terms of families of vector fields that commute
approximately with d-bar. 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.
