The boundedness of Riesz transforms for Hermite expansions on the Hardy spaces

Let L=−Δ+2|x| be a Hermite operator, where Δ is the Laplacian on Rd. In this paper, we first characterize the Hardy spaces associated with L by a new version of area integral. Then, we use it to prove the boundedness of Riesz transforms , j=1,2,… for L on . Moreover, we characterize the Hardy space by . This gives a negative answer to a question asked by Thangavelu.