  In this paper, we study transcendental aspects of the cohomology groups of
adjoint bundles of log canonical pairs, aiming to establish an analytic theory
for log canonical singularities. As a result, in the case of purely log
terminal pairs, we give an analytic proof of the injectivity theorem originally
proved by the Hodge theory. Our method is based on the theory of harmonic
integrals and the L2-method for the dbar-equation, and it enables us to
generalize the injectivity theorem to the complex analytic setting.
