A remark on Littlewood-Paley theory for the distorted Fourier transform
  We show that the usual Mikhlin multiplier theorem relative to the distorted Fourier transform holds in the range (3/2,3) at least for radial functions and potentials. The restricted range is due to the fact that the Schroedinger operator which gives rise to the distorted Fourier transform may have a zero energy resonance. Consequently, the Littlewood-Paley theorem is shown also only for the range (3/2,3). 
Wilhelm Schlag