Qα−1 spaces for Hermite operator and their applications in a class of Hermite-dissipative equations

Abstract Let H = − Δ + | x | 2 be a Hermite operator acting on L 2 ( R d ) . In this paper, we introduce a class of the Q α − 1 spaces associated with H. As an application, with initial data in Q α − 1 space, we obtain the well-posedness of a class of dissipative equations related to H. In order to get our results, we will prove that the Besov spaces are the real interpolations of the Sobolev spaces associated with H.