Boundedness of Singular Integrals on Hardy Type Spaces Associated with Schrödinger Operators. (6th April 2015) - Dong, Jianfeng; Huang, Jizheng; Liu, Heping
Abstract : LetL = - Δ + V be a Schrödinger operator onR n, n ≥ 3, whereV ≢ 0 is a nonnegative potential belonging to the reverse Hölder classB n / 2 . The Hardy type spacesH L p,   n / ( n + δ )   < p ≤ 1, for someδ > 0, are defined in terms of the maximal function with respect to the semigroup{ e - t L } t > 0 . In this paper, we investigate the bounded properties of some singular integral operators related toL, such asL i γ and∇ L - 1 / 2, on spacesH L p . We give the molecular characterization ofH L p, which is used to establish theH L p -boundedness of singular integrals.