Iterated Commutators for Multilinear Singular Integral Operators on Morrey Space with Non-Doubling Measures

Tie Li, Yinsheng Jiang, Yaoming Niu
2020 Journal of Applied Mathematics and Physics  
Let µ be a non-negative Radon measure on d  which only satisfies the following growth condition that there exists a positive constant C such that Keywords Non-Doubling Measures, Morrey Space, Multilinear Singular Integral Operators, RBMO, Commutator , Q x l Q will be the cube centered at x with side length ( ) l Q . For 0 r > , rQ will denote the cube with the same center as Q and with ( ) ( ) The set of all cubes In this note, we do not as-How to cite this paper: Lisume that µ is doubling.
more » ... t µ is doubling. Nazarov, Treil and Volberg developed the theory of the singular integrals for the measures with growth condition to investigate the analytic capacity on the complex plane [1] [2]. Tolsa showed that the analytic capacity is subadditive and that it is bi-Lipschitz invariant [3] [4] and defined for the growth measures RBMO (regular bounded mean oscillation) space, the Hardy space ghted case). Xu [22] extended the result to the case of the non-doubling measures. Very recently, Tao and He [23] obtained the boundedness of the multilinear Calderón-Zygmund operators on the generalized Morrey spaces over the quasi-metric space of non-homogeneoustype. The aim of this paper is to study the iterated commutators of multilinear singular integral operators on Morrey T. Li et al. spaces with non-doubling measures. Before stating our result, we recall some definitions and notation. Given ( ) 2, p q M µ by ( ) p q M µ . T. Li et al.
doi:10.4236/jamp.2020.81005 fatcat:7ifcut42jvdndbqydwwpw7uvii