Regularity properties of the heat kernel and area integral characterization of Hardy space HL1 related to degenerate Schrödinger operators

In this paper we introduce the area integral associated with the heat semigroup {Tt}t>0 generated by a degenerate Schrödinger operator L. We obtain a regularity estimate of the kernels of the semigroup {Tt}t>0. This regularity, together with a reproducing formula, enables us to establish the area integral characterization of the Hardy space associated with L.