Hardy spaces associated with magnetic Schrodinger operators on strongly Lipschitz domains

Let p is an element of (0, 1], Omega be a strongly Lipschitz domain in R" and A := -(del - i (a) over right arrow) . (del - i (a) over right arrow) + V a magnetic Schrodinger operator on L-2(Omega) satisfying the Dirichlet boundary condition, where (a)over right arrow> := (a(1), . . . , a(n)) is an element of L-Ioc(2) (Omega, R-n) and 0 <= V is an element of L-Ioc(1)(Omega). In this paper, the authors introduce the Hardy space H-A(p)(Omega) by the Lusin area function associated with A and establish its equivalent characterization via the non-tangential maximal function associated with e(-t root A)}(t>0). As applications, the authors obtain the boundedness of the Riesz transforms L(k)A(-1/2), k is an element of {1, . . . , n}, from H-A(p)(Omega) to L-p(Omega) for p is an element of (0,1] and the fractional integral A(-gamma) from H-A(p)(Omega) to H-A(q)(Omega) for 0 < p < q <= 1 and gamma := n/2(1/p - 1/q)), where L-k is the closure of partial derivative/partial derivative x(k) - ia(k) in L-2(Omega). (C) 2012 Elsevier Ltd. All rights reserved.