A New Version Of Carleson Measure Associated With Hermite Operator

Hardy space theory and BMO space theory are one of the important research fields in harmonic analysis,the dual relationship between them is a famous work in harmonic analysis in the last century.Carleson measure characterization of BMO space is an important result about BMO space.This paper defines a new version of Carleson measure associated with Hermite operator and we use it to characterize the dual spaces and predual spaces of the Hardy spaces HLp Rd associated with Hermite operator.This paper is divided into two parts.In the first part,we estimate the integral kernels of Hermite heat semigroups and Poisson semigroups accurately,and then estimate the action of the generalized gradient on the heat kernels and Poisson kernels;In the second part,we use the generalized gradient to define a new Carleson measure,and then use the new version of Carleson measure to characterize the dual spaces and the predual spaces of Hardy space that associated with Hermite operator.