Abstract

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<s<1/2. We deduce a characterization of the space of pointwise multipliers from H˙s(R) to its dual H˙−s(R) in terms of trace measures.

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