Weighted Endpoint Estimates for Commutators of Riesz Transforms Associated with Schrödinger Operators

Yu Liu, Jielai Sheng and Lijuan Wang

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: Let L = −Δ + V be a Schrödinger operator, where Δ is the laplacian on ℝn and the nonnegative potential V belongs to the reverse Hölder class Bs1 for some s1 ≥ (n/2). Assume that ω ∈ A1(ℝn). Denote by HL1(ω) the weighted Hardy space related to the Schrödinger operator L = −Δ + V. Let ℛb = [b, ℛ] be the commutator generated by a function b ∈ BMOθ(ℝn) and the Riesz transform ℛ = ∇(−Δ + V) −(1/2). Firstly, we show that the operator ℛ is bounded from L1(ω) into Lweak1(ω). Secondly, we obtain the endpoint estimates for the commutator [b, ℛ]. Namely, it is bounded from the weighted Hardy space HL1(ω) into Lweak1(ω).

Date: 2013
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https://doi.org/10.1155/2013/281562

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:281562

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