2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75102We characterize the weighted Hardy's inequalities for monotone functions in ${\mathbb R^n_+}.$ In dimension $n=1$, this recovers the classical theory of $B_p$ weights. For $n>1$, the result was only known for the case $p=1$. In fact, our main theorem is proved in the more general setting of partially ordered measure spaces.14 pagesClassical Analysis and ODEs46E30, 46B25text