Abstract
In this paper we solve the tangential Cauchy-Riemann equation with gain in regularity in the usual Holder and L-p spaces, and in the nonisotropic Holder and L-p-Sobolev spaces on a strictly q-convex domain D with smooth boundary in a smooth q-concave generic CR manifold M of arbitrary codimension k >= 1 in a Stein manifold X of complex dimension n >= 2.