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Hardy's inequalities with indices less than $ 1$


Authors: Paul R. Beesack and Hans P. Heinig
Journal: Proc. Amer. Math. Soc. 83 (1981), 532-536
MSC: Primary 26D15
DOI: https://doi.org/10.1090/S0002-9939-1981-0627685-7
MathSciNet review: 627685
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Abstract: In this paper Hardy inequalities are proved between weighted $ {L^p}$, $ {L^q}$ spaces with indices $ p$, $ q$ less than 1. The results are almost characterizations of those weights for which weighted estimates hold.


References [Enhancements On Off] (What's this?)

  • [1] P. R. Beesack, Hardy's inequalities and its extensions, Pacific J. Math. 11 (1961), 31-61. MR 0121449 (22:12187)
  • [2] J. S. Bradley, Hardy inequalities with mixed norms, Canad. Math. Bull. 21 (1978), 405-408. MR 523580 (80a:26005)
  • [3] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, 1959.
  • [4] H. P. Heinig, Variations of Hardy's inequality, Real Anal. Exchange 5 (1979-80), 61-81. MR 557964 (81g:26008)
  • [5] B. Muckenhoupt, Hardy's inequality with weights, Studia Math. 44 (1972), 31-38. MR 0311856 (47:418)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0627685-7
Keywords: Inequality, Hardy operator, weight function, $ {L^p}$-spaces
Article copyright: © Copyright 1981 American Mathematical Society

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