Hardy spaces associated with magnetic Schrödinger operators on strongly Lipschitz domains

Let p∈(0,1]p∈(0,1], ΩΩ be a strongly Lipschitz domain in RnRn and A:=−(∇−ia→)⋅(∇−ia→)+V a magnetic Schrödinger operator on L2(Ω)L2(Ω) satisfying the Dirichlet boundary condition, where a→:=(a1,…,an)∈Lloc2(Ω,Rn) and 0≤V∈Lloc1(Ω). In this paper, the authors introduce the Hardy space HAp(Ω) by the Lusin area function associated with AA and establish its equivalent characterization via the non-tangential maximal function associated with {e−tA}t>0. As applications, the authors obtain the boundedness of the Riesz transforms LkA−12, k∈{1,…,n}k∈{1,…,n}, from HAp(Ω) to Lp(Ω)Lp(Ω) for p∈(0,1]p∈(0,1] and the fractional integral A−γA−γ from HAp(Ω) to HAq(Ω) for 0