Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators

Abstract EN

Let L=-Δ+V be a Schrödinger operator on ℝn (n≥3), where V≢0 is a nonnegative potential belonging to certain reverse Hölder class Bs for s≥n/2.

In this paper, we prove the boundedness of commutators ℛbHf=bℛHf-ℛH(bf) generated by the higher order Riesz transform ℛH=∇2(-Δ+V)-1, where b∈BMOθ(ρ), which is larger than the space BMO(ℝn).

Moreover, we prove that ℛbH is bounded from the Hardy space HL1(ℝn) into weak Lweak1(ℝn).