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

Nicola Arcozzi·Sorina Barza·Josep L. Garcia-Domingo·Javier Soria
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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.

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Nicola Arcozzi, Sorina Barza, Josep L. Garcia-Domingo, Javier Soria. 2005-05-06. Hardy's inequalities for monotone functions on partially ordered measure spaces. https://arxiv.org/abs/math/0505105

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