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

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

2010-03-16

arxiv.org/abs/1003.3166v1

Mathematics

Functional Analysis

8 pages

Scientific paper

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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