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In this note we continue giving the characterisation of weights fortwo-weight Hardy inequalities to hold on general metric measure spacespossessing polar decompositions. Since there may be no differentiable structureon such spaces, the inequalities are given in the integral form in the spiritof Hardy's original inequality. This is a continuation of our paper [M.Ruzhansky and D. Verma. Hardy inequalities on metric measure spaces, Proc. R.Soc. A., 475(2223):20180310, 2018] where we treated the case $p\leq q$. Herethe remaining range $p>q$ is considered, namely, $0<q<p$, $1<p<\infty.$ We giveexamples obtaining new weighted Hardy inequalities on $\mathbb R^n$, onhomogeneous groups, on hyperbolic spaces, and on Cartan-Hadamard manifolds. Wenote that doubling conditions are not required for our analysis.

Hardy inequalities on metric measure spaces, II: The case $p>q$