Hardy-Sobolev spaces associated with Hermite expansions and interpolation

Let A=−Δ+|x|2 be a Hermite operator, where Δ is the Laplacian on Rd. In this paper, we first define the Hardy-Sobolev spaces associated with Hermite expansions, then we give the atomic decomposition and the real interpolation with Sobolev spaces. As an application, we consider the endpoint version of the div-curl theorem for the Hermite operator.