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

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

2005-05-06

arxiv.org/abs/math/0505105v1

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

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.

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