A new version of Carleson measure associated with Hermite operator.

Abstract

Let $L=-\Delta +{\left|x\right|}^2$ be a Hermite operator, where Δ is the Laplacian on $R^d$ . 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 $H_L^p\left(R^d\right)$ associated with L.