On $L^2$-boundedness of pseudo-multipliers associated to the Grushin operator
Analysis of PDEs
2024-02-19 v3 Classical Analysis and ODEs
Functional Analysis
Abstract
In this article we define analogues of pseudo-differential operators associated to the joint functional calculus of the Grushin operator using their spectral resolution, and study Calder\'on--Vaillancourt-type theorems for these operators.
Keywords
Cite
@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}
}
Comments
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