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arXiv · 1610.07032

Anisotropic $L^{2}$-weighted Hardy and $L^{2}$-Caffarelli-Kohn-Nirenberg inequalities

Michael Ruzhansky·Durvudkhan Suragan
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Abstract

We establish sharp remainder terms of the $L^{2}$-Caffarelli-Kohn-Niren\-berg inequalities on homogeneous groups, yielding the inequalities with best constants. Our methods also give new sharp Caffarelli-Kohn-Nirenberg type inequalities in $\mathbb{R}^{n}$ with arbitrary quasi-norms. We also present explicit examples to illustrate our results for different weights and in abelian cases.

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Michael Ruzhansky, Durvudkhan Suragan. 2016-10-22. Anisotropic $L^{2}$-weighted Hardy and $L^{2}$-Caffarelli-Kohn-Nirenberg inequalities. https://arxiv.org/abs/1610.07032

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