关于带权分数阶Poincaré-Sobolev不等式中的BBM现象
经典分析与常微分方程
2022-04-20 v2 偏微分方程分析
摘要
本文统一并改进了Bourgain、Brezis与Mironescu的部分结果,以及Fabes、Kenig与Serapioni的带权Poincaré-Sobolev估计。更确切地说,在一些温和的自然限制下,我们得到了分数阶情形中Poincaré-Sobolev型不等式及Hardy型不等式的带权对应形式。我们所获结果的一个主要特征是,我们追踪了当分数参数趋于时相关常数的行为。我们的主要方法基于来自调和分析的技术,涉及广义Poincaré不等式的自改进性质。
引用
@article{arxiv.2201.11712,
title = {On the BBM-phenomenon in fractional Poincar\'e-Sobolev inequalities with weights},
author = {Ritva Hurri-Syrjänen and Javier C. Martínez-Perales and Carlos Pérez and Antti V. Vähäkangas},
journal= {arXiv preprint arXiv:2201.11712},
year = {2022}
}
备注
In the first version of the paper there was an issue with inequality (1.8) since the factor $\delta^{\frac{1}{p}}$ on the right-hand side has to be omitted in the general case. This is certainly not relevant to our contribution in the paper, but in order to correct this issue and not propagate the imprecision, we decided to remove the factor $\delta^{1/p}$ from every incorrect appearance