Boundedness of Singular Integrals on Hardy Type Spaces Associated with Schrödinger Operators

Abstract EN

Let L = - Δ + V be a Schrödinger operator on R n , n ≥ 3 , where V ≢ 0 is a nonnegative potential belonging to the reverse Hölder class B n / 2 .

The Hardy type spaces H L p , n / ( n + δ ) < p ≤ 1, for some δ > 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 to L , such as L i γ and ∇ L - 1 / 2 , on spaces H L p .

We give the molecular characterization of H L p , which is used to establish the H L p -boundedness of singular integrals.