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Published in:
2014 | OriginalPaper | Chapter
Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 3
Authors : S. Abramovich, L.-E. Persson
Published in: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation
Publisher: Springer Basel
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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.