Hardy–Rellich identities with Bessel pairs

  • Tuan Duy Nguyen
  • Nguyen Lam-HoangEmail author
  • Anh Triet Nguyen


We prove an identity that implies the classical Rellich inequality as well as several improved versions of Rellich type inequalities. Moreover, our equality gives a simple perception of Rellich type inequalities as well as the nonexistence of extremizers.


Hardy–Rellich type inequalities Bessel pair Remainder term Optimizer 

Mathematics Subject Classification

26D10 46E35 35A23 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tuan Duy Nguyen
    • 1
  • Nguyen Lam-Hoang
    • 2
    • 3
    Email author
  • Anh Triet Nguyen
    • 4
  1. 1.Department of Fundamental SciencesUniversity of Finance-MarketingDist. 7, HCM CityVietnam
  2. 2.Division of Computational Mathematics and EngineeringInstitute for Computational Science, Ton Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  4. 4.Institute of Fundamental and Applied Sciences, Duy Tan UniversityDa NangVietnam

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