Geodesic
Reverse integral Hardy inequality on metric measure spaces
Aidyn Kassymov1 ; Michael Ruzhansky2 ; Durvudkhan Suragan3
1 Ghent University, Department of Mathematics, and Institute of Mathematics and Mathematical Modeling, Kazakhstan, and Al-Farabi Kazakh National University
2 Ghent University, Department of Mathematics, and Queen Mary University of London, School of Mathematical Sciences
3 Nazarbayev University, School of Science and Technology, Department of Mathematics
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 39-55.

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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.  
DOI : 10.54330/afm.112455
Keywords: Reverse integral Hardy inequality, reverse Minkowski inequality, metric measure space, homogeneous Lie group, hyperbolic space, Cartan-Hadamard manifolds

Aidyn Kassymov 1 ; Michael Ruzhansky 2 ; Durvudkhan Suragan 3

1 Ghent University, Department of Mathematics, and Institute of Mathematics and Mathematical Modeling, Kazakhstan, and Al-Farabi Kazakh National University
2 Ghent University, Department of Mathematics, and Queen Mary University of London, School of Mathematical Sciences
3 Nazarbayev University, School of Science and Technology, Department of Mathematics 
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Aidyn Kassymov; Michael Ruzhansky; Durvudkhan Suragan. Reverse integral Hardy inequality on metric measure spaces. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 39-55. doi : 10.54330/afm.112455. http://geodesic.mathdoc.fr/articles/10.54330/afm.112455/

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