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Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 1133–1141 | Cite as

An Improvement of Hardy’s Inequality for Hilbert Space Operators

  • Mohsen Kian
  • Mohsen Rostamian DelavarEmail author
Article
  • 74 Downloads

Abstract

In this paper, using the notion of superquadratic functions and operator valued mappings, we give an improvement of the Hardy inequality for Hilbert space operators. Then we apply our results to the classical Hardy inequality. In particular, we obtain an estimation for the positive expression
$$\begin{aligned} \left( \frac{p}{p-1}\right) ^p\int _{0}^{\infty }f(x)^pdx - \int _{0}^{\infty }\left( \frac{1}{x}\int _{0}^{x}f(t)dt\right) ^pdx, \end{aligned}$$
where \(p\ge 1\) and f is a positive p-integrable function on \((0,\infty )\).

Keywords

Hardy inequality p-integrable Weakly measurable mapping Superquadratic function 

Mathematics Subject Classification

Primary 26D15 Secondary 47A56 

Notes

Acknowledgements

The authors are thankful to the handling editor and the anonymous referees for useful comments and suggestions.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Basic SciencesUniversity of BojnordBojnordIran

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