  In this article we prove the existence of solutions to the coagulation
equation with singular kernels. We use weighted L^1-spaces to deal with the
singularities in order to obtain regular solutions. The Smoluchowski kernel is
covered by our proof. The weak L^1 compactness methods are applied to suitably
chosen approximating equations as a base of our proof. A more restrictive
uniqueness result is also mentioned.
