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Mathematische Annalen

, Volume 334, Issue 3, pp 489–531 | Cite as

Weighted Hardy inequalities for decreasing sequences and functions

  • G. Bennett
  • K.-G. Grosse-ErdmannEmail author
Article

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.

Mathematics Subject Classification (2000)

26D15 47B37 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Fachbereich MathematikFernuniversität HagenHagenGermany

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