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Let $T_m$ be the $m$-th Calder\'on-Zygmund type singular integral. In thepaper, we consider the boundedness of $T_m$ on the generalized product localMorrey spaces $LM_{p_1,\varphi_1}^{\{x_0\}}\timesLM_{p_2,\varphi_2}^{\{x_0\}}\times\dots\times LM_{p_m,\varphi_m}^{\{x_0\}}.$And, the boundedness of the commutators of $T_m$ with local Campanato functionsis obtained, also.

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