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Some Generalisations and Refinements of the Hardy Inequality

  • H. Heinig
  • A. Kufner
  • L. E. Persson
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 430)

Abstract

Some recent results connected with the one-dimensional Hardy operator are given. Namely, some fractional order analogues of the classical Hardy inequality are discussed, and results concerning the two-dimensional Hardy operator are extended to Hardy operators defined on 1ℝ M × ℝ N . The main tools are the interpolation theory and some direct approaches for the fractional order case, and a recently derived N-dimensional Hardy inequality for operators on ℝ N .

Key words and phrases

Hardy inequalities Fractional order derivatives Weighted Lebesgue spaces More-dimensional inequalities 

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • H. Heinig
    • 1
  • A. Kufner
    • 2
  • L. E. Persson
    • 3
  1. 1.Department of MathematicsMcMaster UniversityHamiltonCanada
  2. 2.Mathematical InstituteAcademy of SciencesPragueCzech Republic
  3. 3.Department of MathematicsLuleå UniversityLuleåSweden

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