Hardy's inequalities for monotone functions on partially ordered measure spaces

Abstract

We 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 pages

References in corpus (1)

• Mixed norm and multidimensional Lorentz spaces