Anisotropic L-2-weighted Hardy and L-2-Caffarelli-Kohn-Nirenberg inequalities

作者：Ruzhansky Michael^*; Suragan Durvudkhan

来源：Communications in Contemporary Mathematics, 2017, 19(6): 1750014.

DOI：10.1142/S0219199717500146

• Caffarelli-Kohn-Nirenberg inequality
• Hardy inequality
• weighted inequalities
• homogeneous Lie group
• sharp remainder

We establish sharp remainder terms of the L-2-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 R-n with arbitrary quasi-norms. We also present explicit examples to illustrate our results for different weights and in abelian cases.

• 出版日期2017-12