The boundedness of Fractional Hardy-Littlewood maximal operator on variable lp(Z) spaces using Calderon-Zygmund decomposition

In this paper, we prove strong type, weak type inequalities of Hardy-Littlewood maximal operator and fractional Hardy-Littlewood maximal operator on variable sequence spaces lp(Z). This is achieved using Calderon-Zygmund decomposition for sequences, properties of modular functional and Log Holder continuity.