A new version of Carleson measure associated with Hermite operator

Abstract

Abstract Let L=−Δ+|x|2 $L=-\Delta+|x|^{2}$ be a Hermite operator, where Δ is the Laplacian on Rd $\mathbb {R}^{d}$. In this paper we define a new version of Carleson measure associated with Hermite operator, which is adapted to the operator L. Then, we will use it to characterize the dual spaces and predual spaces of the Hardy spaces HLp(Rd) $H_{L}^{p}(\mathbb {R}^{d})$ associated with L.

Keywords

• Hermite operator
• Carleson measure
• Dual space
• Hardy space
• BMO space