Abstract

Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bT f − T(bf) on Lp, p ∈ (1,∞), where T is a Calderon-Zygmund operator related to the admissible function ρ and b ∈ BMOθ(X) ⊇ BMO(X). Moreover, they prove that Tb is bounded from the Hardy space Hρ1 (X) into the weak Lebesgue space Lweak1(X). This can be used to deal with the Schrodinger operators and Schrodinger type operators on the Euclidean space ℝn and the sub-Laplace Schrodinger operators on the stratified Lie group \(\mathbb{G}\).

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