Abstract
We establish sharp remainder terms of the [Formula: see text]-Caffarelli–Kohn–Nirenberg inequalities on homogeneous groups, yielding the inequalities with best constants. Our methods also give new sharp Caffarelli–Kohn–Nirenberg-type inequalities in [Formula: see text] with arbitrary quasi-norms. We also present explicit examples to illustrate our results for different weights and in abelian cases.
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