The Hardy-Littlewood Maximal Operator on Discrete Weighted Morrey Spaces

Abstract: In this paper, we introduce a discrete version of weighted Morrey spaces, and discuss the inclusion relations of these spaces. In addition, we obtain the boundedness of discrete weighted Hardy-Littlewood maximal operators on discrete weighted Lebesgue spaces by establishing a discrete Calder\'on-Zygmund decomposition for weighted $l^{1$-sequences.} Furthermore, the boundedness of discrete Hardy-Littlewood maximal operators on discrete weighted Morrey spaces is established.