The Hardy–Littlewood maximal operator on discrete weighted Morrey spaces

We introduce a discrete version of weighted Morrey spaces,and discuss the inclusion relations of these spaces. In addition, we obtain theboundedness of discrete weighted Hardy-Littlewood maximal operators on discreteweighted Lebesgue spaces by establishing a discrete Calderón-Zygmund decompositionfor weighted \(l^1\) $l^1$ -sequences. Furthermore, the necessary and sufficientconditions for the boundedness of the discrete Hardy-Littlewood maximal operatorson discrete weighted Morrey spaces are discussed. Particularly, the necessaryand sufficient conditions are also discussed for the discrete power weights.