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arXiv · 2602.04601

Caffarelli-Kohn-Nirenberg Inequalities in Weak Lebesgue Spaces

Dinghuai Wang
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Abstract

By employing harmonic analysis techniques, we derive weak-type Caffarelli-Kohn-Nirenberg inequalities under natural parameter conditions. A key feature of these weak-type versions is that they remain valid even at critical parameter values where the classical inequalities fail. As an important corollary, we obtain weak-type Hardy inequalities that hold true even in the critical dimension \(d = p\). The methods developed here are sufficiently flexible to handle homogeneous, non-homogeneous and anisotropic weights, providing a unified approach to various endpoint cases in interpolation theory.

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Dinghuai Wang. 2026-02-04. Caffarelli-Kohn-Nirenberg Inequalities in Weak Lebesgue Spaces. https://arxiv.org/abs/2602.04601

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