  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.
