局部到全局的弱 (1,1) 型论证及其在傅里叶积分算子中的应用
偏微分方程分析
2021-04-27 v3
摘要
在本工作中，我们为已知局部一致为弱 (1,1) 型的积分算子的全局弱 (1,1) 型提供了一个判据。作为一个应用，我们建立了一类傅里叶积分算子的全局弱 (1,1) 型。尽管局部结果来自 Tao [33] 对阶为 的傅里叶积分算子的工作，我们给出了自然充分条件以将其推广到相应的全局估计。
引用
@article{arxiv.2103.12143,
title = {A local-to-global weak (1,1) type argument and applications to Fourier integral operators},
author = {Duván Cardona and Michael Ruzhansky},
journal= {arXiv preprint arXiv:2103.12143},
year = {2021}
}
备注
Unfortunately, we have found a mistake in the proof of Theorem 1.2, that is the main theorem of this work. We claim in page 10, below of (2.5) that the uniform estimate of the weak L^1 norm of T at any atom is enough for concluding the proof, but this is not the case, because the weak L^1 space is not normable