Year: 2023
Type: preprint
Abstract: We study a specific class of Fourier integral operators characterized by symbols belonging to the multi-parameter Hörmander class $\mathbf{S}^m(\R^{ n_1} \times \R^{ n_2} \times \cdots \times \R^{n_d} )$, where $n= n_1 + n_2 +\cdots + n_d$. Our investigation focuses on cases where the phase function $Φ(x,ξ)$ can be decomposed into a sum of individual components $Φ_i(x_i,ξ_i)$, with each component satisfying a non-degeneracy condition. We extend the Seeger-Sogge-Stein theorem under the condition that the dimension $ n_i \ge 2$ for each $1\le i \le d$. As a corollary, we obtain the boundedness of multi-parameter Fourier integral operators on local Hardy spaces, Lipschitz spaces, and Sobolev spaces.
Source: arXiv (Cornell University)
Author: Cheng, Jinhua
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4385328022