关于与 Grushin 算子相关的伪乘子的 $L^2$ 有界性
偏微分方程分析
2024-02-19 v3 经典分析与常微分方程
泛函分析
摘要
在本文中，我们利用 Grushin 算子的联合函数演算的谱分解定义了与其相关的伪微分算子的类比，并研究了这些算子的 Calderón--Vaillancourt 型定理。
引用
@article{arxiv.2111.10098,
title = {On $L^2$-boundedness of pseudo-multipliers associated to the Grushin operator},
author = {Sayan Bagchi and Rahul Garg},
journal= {arXiv preprint arXiv:2111.10098},
year = {2024}
}
备注
Subsection 2.1 is new, discussing the notion of pseudo-multipliers for non-negative self-adjoint operators on $\sigma$-finite measure spaces. We show its relation with that for specific operators such as the Grushin operator. This discussion is particularly helpful in understanding our definition of symbol classes. Related changes occur in Subsection 1.3 too, resulting in an improved reading