Boundedness Of Both Discrete Hardy And Hardy-Littlewood Maximal Operators Via Muckenhoupt Weights

We employ the self-improving property (backward propagation) for the discrete Muckenhoupt class A(p), to prove that both discrete Hardy and discrete Hardy-Littlewood maximal operators are bounded on the usual weighted Lebesgue space l(u)(p)(Z(+)) if and only if the weight u belongs to A(p). Some weak boundedness results for the Hardy-Littlewood maximal operators will also be discussed. To the best of the authors' knowledge, the results are essentially new and have not been discussed before.