Boundedness of commutators generated by m-th Calderón-Zygmund type singular integrals and local Campanato functions on generalized local Morrey spaces

Abstract

Let $T_m$ be the $m$-th Calderón-Zygmund type singular integral. In the paper, we consider the boundedness of $T_m$ on the generalized product local Morrey spaces $L{M}_{p_1,{\phi }_1}^{\{x_0\}}\times L{M}_{p_2,{\phi }_2}^{\{x_0\}}\times \cdots \times L{M}_{p_m,{\phi }_m}^{\{x_0\}}.$ And, the boundedness of the commutators of $T_m$ with local Campanato functions is obtained, also.