分数阶矢量 Riesz 变换与加倍测度的双权 L^{p} 不等式
经典分析与常微分方程
2024-05-14 v6
摘要
若 T 为分数阶矢量 Riesz 变换，1<p<∞，且 sigma 与 omega 为加倍测度，则双权 L^{p} 范数不等式成立当且仅当 Hytönen 与 Vuorinen 的二次三元检验条件成立。我们还证明这些二次三元检验条件可放宽为二次局部检验条件、二次偏移 Muckenhoupt 条件以及二次弱有界性性质。
引用
@article{arxiv.2211.01920,
title = {Two weight L^{p} inequalities for fractional vector Riesz transforms and doubling measures},
author = {Eric T. Sawyer and Brett D. Wick},
journal= {arXiv preprint arXiv:2211.01920},
year = {2024}
}
备注
51 pages, thanks to a referee for many helpful comments leading to the current version. The main change in the current argument is the use of Haar wavelets instead of Alpert wavelets. This has no effect on the main theorem, but does eliminate one of our remarks regarding where the restriction to vector Riesz transforms is needed. Thanks also to I. Uriarte-Tuero, M. Alexis and J.-L. Luna-Garcia