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Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 3

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Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 236))

Abstract

For usual Hardy type inequalities the natural “breaking point” (the parameter value where the inequality reverses) is p = 1. Recently, J. Oguntuase and L.-E. Persson proved a refined Hardy type inequality with breaking point at p = 2. In this paper we show that this refinement is not unique and can be replaced by another refined Hardy type inequality with breaking point at p = 2. Moreover, a new refined Hardy type inequality with breaking point at p = 3 is obtained. One key idea is to prove some new Jensen type inequalities related to convex or superquadratic funcions, which are also of independent interest.

Mathematics Subject Classification (2010). 26D15.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Haifa, Haifa, 34987, Israel

    S. Abramovich

  2. Department of Mathematics, Lulea University of Technology, SE-971871, Lulea, Sweden

    L.-E. Persson

  3. Narvik University College, 385, N-8505, Narvik, Norway

    L.-E. Persson

Authors
  1. S. Abramovich
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  2. L.-E. Persson
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Corresponding author

Correspondence to S. Abramovich .

Editor information

Editors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Manuel Cepedello Boiso

  2. Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden

    Håkan Hedenmalm

  3. Department of Mathematics & Computer Sci, Free University Amsterdam, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  4. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Alfonso Montes Rodríguez

  5. Department of Mathematics, Brown University, Providence, Rhode Island, USA

    Sergei Treil

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Abramovich, S., Persson, LE. (2014). Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 3. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodríguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_1

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