Characterizations of the Hardy space $\mathcal H_{\rm FIO}^{1}(\mathbb R^{n})$ for Fourier integral operators
Volume 270 / 2023
Studia Mathematica 270 (2023), 175-207
MSC: Primary 42B35; Secondary 35S30, 42B30.
DOI: 10.4064/sm220217-19-9
Published online: 12 December 2022
Abstract
The Hardy spaces for Fourier integral operators $\mathcal H_{\rm FIO}^{p}(\mathbb R^{n})$, for $1\leq p\leq \infty $, were introduced by Smith and by Hassell et al. In this article, we give several equivalent characterizations of $\mathcal H_{\rm FIO}^{1}(\mathbb R^{n})$, for example in terms of Littlewood–Paley $g$ functions and maximal functions. We also give several applications of the characterizations.
