Hardy-type space estimates for multilinear commutators of Calderón–Zygmund operators on nonhomogeneous metric measure spaces

Abstract

Let (X,d,μ) be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. Let T be a Calderón–Zygmund operator and let b→:=(b1,…,bm) be a finite family of \widetilde{RBMO}(μ) functions. In this article, the authors establish the boundedness of the multilinear commutator Tb→, generated by T and b→ from the atomic Hardy-type space H˜fin,b→,m,ρ1,q,m+1(μ) into the Lebesgue space L1(μ). The authors also prove that Tb→ is bounded from the atomic Hardy-type space H˜fin,b→,m,ρ1,q,m+2(μ) into the atomic Hardy space H˜1(μ) via the molecular characterization of H˜1(μ).