分数阶向量 Riesz 变换与倍增权重的双权重 Sobolev 范数不等式
经典分析与常微分方程
2024-04-05 v2
摘要
我们证明了分数阶向量 Riesz 变换从一个加权 Sobolev 空间映射到另一个的 T1 定理，其中权重为欧氏空间上的倍增测度。有界性由经典的 A_2 条件以及对立方体指示函数的两个对偶测试条件刻画。我们还证明了当测度倍增时各种加权 Sobolev 范数的等价性，而这一点在一般情况下不成立。
引用
@article{arxiv.2207.14684,
title = {Two weight Sobolev norm inequalities for fractional vector Riesz transforms and doubling weights},
author = {Eric T. Sawyer and Brett D. Wick},
journal= {arXiv preprint arXiv:2207.14684},
year = {2024}
}
备注
An error was found in the treatment of the stopping form in the previous version, and as a result, the T1 theorem is weakened - it applies only to fractional vector Riesz transforms now. The other main theorems remain unchanged