Bilinear forms on homogeneous Sobolev spaces

In this paper we characterize the boundedness of the bilinear form defined by(f,g)∈H˙s(R)×H˙s(R)→∫R(−Δ)s/2(fg)(x)(−Δ)s/2(b)(x)dx, in the product of homogeneous Sobolev spaces H˙s(R)×H˙s(R), 0