Abstract
We obtain a complete characterization of the weights for which Hardy's inequality holds on the cone of non-increasing sequences. Our proofs translate immediately to the analogous inequality for non-increasing functions, thereby also completing the investigation in that direction. As an application of our results we characterize the boundedness of the Hardy-Littlewood maximal operator on Lorentz sequence spaces.
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Bennett, G., Grosse-Erdmann, KG. Weighted Hardy inequalities for decreasing sequences and functions. Math. Ann. 334, 489–531 (2006). https://doi.org/10.1007/s00208-005-0678-7
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DOI: https://doi.org/10.1007/s00208-005-0678-7