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arXiv · 2608.22986

From weighted Carlson-Levin inequalities to weighted Gagliardo-Nirenberg inequalities

Francesco Pagliarin·Nikita Simonov
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Abstract

We study weighted Carlson-Levin inequalities on cones, computing the optimal constant and classifying optimizers via an Entropy method. The limiting case of a logarithmic Carlson-Levin inequality is also treated. As a Corollary, we obtain a rigidity result for a weighted Gagliardo-Nirenberg inequality. We conclude with some examples involving monomial weights.

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Francesco Pagliarin, Nikita Simonov. 2026-08-24. From weighted Carlson-Levin inequalities to weighted Gagliardo-Nirenberg inequalities. https://arxiv.org/abs/2608.22986

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