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arXiv · 1003.3166

On the necessity of the assumptions used to prove Hardy-Littlewood and Riesz Rearrangement Inequalities 1

Hichem Hajaiej
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Abstract

We prove that supermodularity is a necessary condition for the generalized Hardy- Littlewood and Riesz rearrangement inequalities. We also show the necessity of the monotonicity of the kernels involved in the Riesz{type integral.

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Hichem Hajaiej. 2010-03-16. On the necessity of the assumptions used to prove Hardy-Littlewood and Riesz Rearrangement Inequalities 1. https://arxiv.org/abs/1003.3166

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