A weighted L^2 estimate of Commutators of Bochner-Riesz Operators for Hermite operator

Let H be the Hermite operator -Δ+|x|^2 on $\mathbb{R}$^n. We prove a weighted L^2 estimate of the maximal commutator operator \sup_{R>0}|b, S_R^λ(H)|, where b, S_R^λ(H) = bS_R^λ(H) f - S_R^λ(H)(bf) is the commutator of a BMO function b and the Bochner-Riesz means S_R^λ(H) for the Hermite operator H. As an application, we obtain the almost everywhere convergence of b, S_R^λ(H) for large λand f\in L^p($\mathbb{R}$^n).