Boundedness of multilinear commutators of Calderón-Zygmund operators on Orlicz spaces over non-homogeneous spaces
Let \((\mathcal{X},d,\mu)\) be a non-homogeneous space. In a recent paper of \textit{T. A. Bui} and \textit{X. T. Duong} [J. Geom. Anal. 23, No.~2, 895--932 (2013; Zbl 1267.42013)], the \(L^p(\mu)\)-boundedness of commutators of Calderón-Zygmund operators with RBMO\((\mu)\) functions was obtained under the assumption that there is \(m\in (0,\infty)\) such that \(\lambda(x,ar)=a^m\lambda(x,r)\) for all \(x\in \mathcal{X}\) and \(a,r\in (0,\infty)\), where \(\lambda\) is the dominating function of the measure \(\mu\). In this paper, the authors essentially improve the above result and prove that, without the above condition, the multilinear commutators of Calderón-Zygmund operators with RBMO\((\mu)\) functions are bounded on some Orlicz spaces, including \(L^p(\mu)\) with \(1<p<\infty\). The authors also obtain a weak type estimate for multilinear commutators of Calderón-Zygmund operators with special Orlicz-type functions.
scientific article; zbMATH DE number 6137999