Reverse integral Hardy inequality on metric measure spaces

Authors

  • Aidyn Kassymov Ghent University, Department of Mathematics, and Institute of Mathematics and Mathematical Modeling, Kazakhstan, and Al-Farabi Kazakh National University
  • Michael Ruzhansky Ghent University, Department of Mathematics, and Queen Mary University of London, School of Mathematical Sciences
  • Durvudkhan Suragan Nazarbayev University, School of Science and Technology, Department of Mathematics

DOI:

https://doi.org/10.54330/afm.112455

Keywords:

Reverse integral Hardy inequality, reverse Minkowski inequality, metric measure space, homogeneous Lie group, hyperbolic space, Cartan-Hadamard manifolds

Abstract

In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, we give necessary and sufficient conditions for the weighted reverse Hardy inequality to be true. The main tool in our proof is a continuous version of the reverse Minkowski inequality. In addition, we present some consequences of the obtained reverse Hardy inequality on the homogeneous groups, hyperbolic spaces and Cartan-Hadamard manifolds.

 

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Published

2021-11-29

Issue

Vol. 47 No. 1 (2022)

Section

Articles

License

Copyright (c) 2021 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Kassymov, A., Ruzhansky, M., & Suragan, D. (2021). Reverse integral Hardy inequality on metric measure spaces. Annales Fennici Mathematici, 47(1), 39-55. https://doi.org/10.54330/afm.112455