Reverse integral Hardy inequality on metric measure spaces. (English) Zbl 1490.46035
Summary: 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.
MSC:
| 46E36 | Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces |
| 43A80 | Analysis on other specific Lie groups |
| 22E30 | Analysis on real and complex Lie groups |
| 30L99 | Analysis on metric spaces |
Keywords:
reverse integral Hardy inequality; reverse Minkowski inequality; metric measure space; homogeneous Lie group; hyperbolic space; Cartan-Hadamard manifoldsReferences:
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