  The purpose of this paper is to establish an injectivity theorem generalized
to pseudo-effective line bundles with transcendental (non-algebraic) singular
hermitian metrics and multiplier ideal sheaves. As an application, we obtain a
Nadel type vanishing theorem. For the proof, we study the asymptotic behavior
of the harmonic forms with respect to a family of regularized metrics, and give
a method to obtain L2-estimates of solutions of the dbar-equation by using the
de Rham-Weil isomorphism between the dbar-cohomology and the check{C}ech
cohomology.
