Weighted anisotropic Hardy and Rellich type inequalities for general vector fields

  • Michael Ruzhansky
  • Bolys SabitbekEmail author
  • Durvudkhan Suragan


In this paper, we establish the weighted anisotropic Hardy and Rellich type inequalities with boundary terms for general (real-valued) vector fields. As consequences, we derive new as well as many of the fundamental Hardy and Rellich type inequalities which are known in different settings.


Vector fields Hardy inequality Rellich inequality Picone identity Uncertainty principle 

Mathematics Subject Classification

35A23 35H20 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics: Analysis, Logic and Discrete MathematicsGhent UniversityGhentBelgium
  2. 2.School of Mathematical SciencesQueen Mary University of LondonLondonUK
  3. 3.Institute of Mathematics and Mathematical ModelingAlmatyKazakhstan
  4. 4.Department of Mechanics and MathematicsAl-Farabi Kazakh National UniversityAlmatyKazakhstan
  5. 5.Department of MathematicsNazarbayev UniversityAstanaKazakhstan

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