On scales of Sobolev spaces associated to generalized Hardy operators (Q2231127)

The author considers the fractional Laplacian with Hardy potential and compares the scale of homogeneous $L_p$ Sobolev spaces generated by this operator with the ordinary homogeneous Sobolev spaces. For the proof he makes use of a generalized Hardy inequality, a reversed Hardy inequality expressed in terms of square functions, and a Hörmander multiplier theorem which is proven for positive coupling constants.