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

  • S. AbramovichEmail author
  • L.-E. Persson
Conference paper
Part of the Operator Theory: Advances and Applications book series (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.

Keywords

Inequalities refined Hardy type inequalities convex functions superquadratic functions Jensen type inequalities. 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael
  2. 2.Department of MathematicsLulea University of TechnologyLuleaSweden
  3. 3.Narvik University CollegeNarvikNorway

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