Characterizations of the Hardy space $\mathcal{H}_{FIO}^{1}(\mathbb{R}^{n})$ for Fourier Integral Operators

Zhijie Fan, Naijia Liu, Jan Rozendaal, Liang Song

Published 2019-08-05Version 1

The Hardy spaces for Fourier integral operators $\mathcal{H}_{FIO}^{p}(\mathbb{R}^{n})$, for $1\leq p\leq \infty$, were introduced by H.~Smith in \cite{Smith98a} and A.~Hassell et al.~in \cite{HaPoRo18}. In this article, we give several equivalent characterizations of $\mathcal{H}_{FIO}^{1}(\mathbb{R}^{n})$, for example in terms of Littlewood--Paley g functions and maximal functions. This answers a question from [Rozendaal,2019].