论文标题
Caffarelli-Kohn-Nirenberg的身份，不平等及其稳定性
Caffarelli-Kohn-Nirenberg identities, inequalities and their stabilities
论文作者
论文摘要
我们建立了一个不平等的单参数家族，其中包含耐力不平等（当参数为1）和caffarelli-kohn-nirenberg不平等现象（当参数是最佳时）。此外，我们以确切的剩余来研究这些结果，以直接理解敏锐的常数，以及Hardy不平等和Caffarelli-Kohn-Nirenberg的优化者的存在和不存在。作为我们身份的应用，我们建立了一些具有最佳常数的敏锐版本及其可实现的海森堡不确定性原理的稳定性，以及Caffarelli-Kohn-Nirenberg不平等的几个稳定性结果。
We set up a one-parameter family of inequalities that contains both the Hardy inequalities (when the parameter is 1) and the Caffarelli-Kohn-Nirenberg inequalities (when the parameter is optimal). Moreover, we study these results with the exact remainders to provide direct understandings to the sharp constants, as well as the existence and non-existence of the optimizers of the Hardy inequalities and Caffarelli-Kohn-Nirenberg inequalities. As an application of our identities, we establish some sharp versions with optimal constants and theirs attainability of the stability of the Heisenberg Uncertainty Principle and several stability results of the Caffarelli-Kohn-Nirenberg inequalities.
