The -Cauchy problem on pseudoconvex domains and applications.

Let be a complex manifold of dimension and be a weakly pseudoconvex domain with smooth boundary in . Let be a holomorphic line bundle over which is positive on a neighborhood of . Let be the -times tensor product of for positive integer . The purpose of this paper is to study the -problem with support conditions in for forms of type , with values in . Applications to the -problem for smooth forms on boundaries of are given. [ABSTRACT FROM AUTHOR]