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Multiple Hardy–Littlewood Integral Operator Norm Inequalities

  • J. C. Kuang
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 151)

Abstract

How to obtain the sharp constant of the Hardy–Littlewood inequality remains unsolved. In this paper, the new analytical technique is to convert the exact constant factor to the norm of the corresponding operator, the multiple Hardy–Littlewood integral operator norm inequalities are proved. As its generalizations, some new integral operator norm inequalities with the radial kernel on n-dimensional vector spaces are established. The discrete versions of the main results are also given.

Notes

Acknowledgement

The author wishes to express his thanks to Professor Bicheng Yang for his careful reading of the manuscript and for his valuable suggestions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • J. C. Kuang
    • 1
  1. 1.Department of MathematicsHunan Normal UniversityChangshaPeople’s Republic of China

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