分次群上 Sobolev 空间的平均值不等式与刻画
泛函分析
2023-06-16 v5 经典分析与常微分方程
摘要
我们通过 Littlewood-Paley 平方函数以及涉及二阶差分的 Strichartz 泛函，发展了分次 Lie 群上势型 Sobolev 空间的刻画。一些可能具有独立意义的平均值不等式起到了关键作用。事实上，点态一阶不等式在两个方面得到了推广：在 空间上以及通过考虑二阶差分。
引用
@article{arxiv.2109.05064,
title = {Mean Value Inequalities and Characterizations of Sobolev spaces on graded groups},
author = {Pablo De Nápoli and Rocío Díaz Martín},
journal= {arXiv preprint arXiv:2109.05064},
year = {2023}
}
备注
We extended the abstract. We corrected a definition of Sobolev spaces defined by derivatives $\mathbb{W}_{p;k}(\mathbb{G})$ on page 1 (suitable for Theorem 3.6). We added the corresponding reference [R Burns. "Sobolev spaces on Lie groups". PhD thesis. The Australian National University, 1991. The definition of inhomogeneous Sobolev spaces of potential type remains the same