In this paper, we conduct a comprehensive study on the boundedness properties of commutators generated by a BMO function and generalized Calderón-Zygmund operator. Specifically, we analyze their mapping behavior from a generalized weighted Morrey space to another generalized weighted Morrey spaces under some conditions on the parameters. Our main objective is to establish novel and refined conditions on the pair of parameter functions that guarantee the boundedness of these commutators on the spaces. The findings presented in this work contribute to a deeper understanding of the interplay between function spaces, weight conditions, and the structure of commutators in harmonic analysis.
Ramadana et al. (Fri,) studied this question.