Area functions on Hardy spaces associated to Schrödinger operators (Q1418268)

Let \(L\) be a Schrödinger operator on \({\mathbb R}^d\) which has the form \[ L=-\Delta+V, \] where \(\Delta\) is the Laplace operator, \(V(x)=\sum_{\beta\leq\alpha}a_\beta x^\beta\) is a nonnegative nonzero polynomial on \({\mathbb R}^d\) and \(\alpha\in {\mathbb N}^d\). In this paper, the author establishes a characterization of atomic Hardy spaces \(H^1_L\) by using area functions, and presents their dual spaces.