L2-Approximation of differential forms by closed ones on smooth hypersurfaces

In this paper we study approximation of ( 0 , q − 1 ) -forms with continuous coefficients in a q-convex domain in C n by ∂ ¯ -closed smooth ( 0 , q − 1 ) -forms in L 2 -norm on level sets of a smooth strictly q-subharmonic function.