(untitled) (Analysis in Theory and Applications, 2017)
Let L = L_0+V be the higher order Schrödinger type operator where L_0 is a homogeneous elliptic operator of order 2m in divergence form with bounded coefficients and V is a real measurable function as multiplication operator (e.g., including (−∆) ^m+V (m∈N) as special examples). In this paper, assume that V satisfies a strongly subcritical form condition associated with L_0, the authors attempt to establish a theory of Hardy space H^p_L(R^n) (0 < p ≤ 1) associated with the higher order Schrödinger type operator L. Specifically, we first define the molecular Hardy space H^p_L(R^n) by the so-called (p,q,ε,M) molecule associated to L and then establish its characterizations by the area integral defined by the heat semigroup e^−tL.