Reverse integral Hardy inequality on metric measure spaces

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.