  We study one-dimensional Schroedinger operators S with real-valued
distributional potentials q in W^{-1}_{2,loc}(R) and prove an extension of the
Povzner-Wienholtz theorem on self-adjointness of bounded below S thus providing
additional information on its domain. The results are further specified for q
in W^{-1}_{2,unif}(R).
