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arXiv · 1908.01448

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

Zhijie Fan·Naijia Liu·Jan Rozendaal·Liang Song
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Abstract

The Hardy spaces for Fourier integral operators $\mathcal{H}_{FIO}^{p}(\mathbb{R}^{n})$, for $1\leq p\leq \infty$, were introduced by Smith in [Smith,1998] and Hassell et al. in [Hassell-Portal-Rozendaal,2020]. 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,2021]. We also give several applications of the characterizations.

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Zhijie Fan, Naijia Liu, Jan Rozendaal, Liang Song. 2019-08-05. Characterizations of the Hardy space $\mathcal{H}_{FIO}^{1}(\mathbb{R}^{n})$ for Fourier integral operators. https://doi.org/10.4064/sm220217-19-9

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