Hardy space $H^1$ associated to Schrödinger operator with potential satisfying reverse Hölder inequality

Abstract

Let $\{T_t{\}}_{t>0}$ be the semigroup of linear operators generated by a Schrödinger operator $–A=\Delta –V$ where $V$ is a nonnegative potential that belongs to a certain reverse Hölder class. We define a Hardy space $H_A^1$ be means of a maximal function associated with the semigroup $\{T_t{\}}_{t>0}$. Atomic and Riesz transforms characterizations of $H_A^1$ are shown.