An Interpolation Theorem on Cycle Spaces for Functions Arising as Integrals of $\bar{\partial }$ Closed Forms

Abstract

It is shown that an interpolation theorem with $L^1$-growth condition holds on the cycle spaces of $q$-complete manifolds with respect to those holomorphic functions ¯ arising as integrals of $\bar{\partial }$-closed $(q-1,q-1)$-forms. The proof is based on the $L^2$-method of Andreotti and Vesentini.