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We characterize the embedding for general weighted Lebesgue spaces of monotone functions by using the analog embedding for discrete monotone sequences indexed over the integers. We then use these results to obtain the boundedness of the discrete Hardy operator and to study the connections with the Hardy classical operator in the continuous setting.doi:10.7146/math.scand.a-14976 fatcat:ltsangw3kfg5leqv5ohjn223bu