On a Reverse Integral Hardy Inequality on Polarisable Metric Measure Space

In this short note, we give reverse integral Hardy inequalities on polarisable metric measure space in the case \(q\leq p<0\) (with two negative exponents). Also, as for applications, we present the reverse Hardy-Littlewood-Sobolev and Stein-Weiss type inequalities with two negative exponents on homogeneous Lie groups and with arbitrary quasi-norm, the result which appears to be new already in the Euclidean space.