The Hardy–Littlewood maximal operator on discrete weighted Morrey spaces

Abstract

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 Calderón-Zygmund decomposition for weighted \(l^1\)-sequences. Furthermore, the necessary and sufficient conditions for the boundedness of the discrete Hardy-Littlewood maximal operators on discrete weighted Morrey spaces are discussed. Particularly, the necessary and sufficient conditions are also discussed for the discrete power weights.