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 Calder\'on-Zygmund type singular integral. In the paper, we consider the boundedness of $T_m$ on the generalized product local Morrey spaces $LM_{p_1,\varphi_1}^{{x_0}}\times LM_{p_2,\varphi_2}^{{x_0}}\times\dots\times LM_{p_m,\varphi_m}^{{x_0}}.$ And, the boundedness of the commutators of $T_m$ with local Campanato functions is obtained, also.