The boundedness of Riesz transforms for Hermite expansions on the Hardy spaces (Q641612)

Let \(L=-\Delta +|x|^2\) be a Hermite operator on \(\mathbb{R}^n\). This paper characterizes the Hardy space \(H^1_L(\mathbb{R}^n)\) associated with \(L\) by a new version of area integral firstly. Then by using this result it proves the boundedness of Riesz transforms \(R^L_j,j=1,2,\dots,n\), for \(L\) on \(H^1_L(\mathbb{R}^n)\). Moreover, it characterizes the Hardy space \(H^1_L(\mathbb{R}^n)\) by \(R^L_j,j=1,2,\dots,n\), which gives a negative answer to a question asked by Thangavelu.