2023/07/26 by Cheng, Jinhua
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2307.14178
We study a specific class of Fourier integral operators characterized by symbols belonging to the multi-parameter Hörmander class Sm(\R n1 × \R n2 × ⋯ × \Rnd ), where n= n1 + n2 +⋯ + nd. Our investigation focuses on cases where the phase function Φ(x,ξ) can be decomposed into a sum of individual components Φi(xi,ξi), with each component satisfying a non-degeneracy condition. We extend the Seeger-Sogge-Stein theorem under the condition that the dimension ni ≥ 2 for each 1≤ i ≤ d. As a corollary, we obtain the boundedness of multi-parameter Fourier integral operators on local Hardy spaces, Lipschitz spaces, and Sobolev spaces.