Inverse spectral problems for Sturm-Liouville operators with singular   potentials, IV. Potentials in the Sobolev space scale
  We solve the inverse spectral problems for the class of Sturm--Liouville operators with singular real-valued potentials from the Sobolev space W^{s-1}_2(0,1), s\in[0,1]. The potential is recovered from two spectra or from the spectrum and norming constants. Necessary and sufficient conditions on the spectral data to correspond to the potential in W^{s-1}_2(0,1) are established. 
R.O.Hryniv, Ya.V.Mykytyuk