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

Abstract

The Hardy spaces for Fourier integral operators ${\mathcal{H}}_{FIO}^p({\mathbb{R}}^n)$, for $1\le p\le \infty$, 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.

24 pages. Minor changes to the previous version. To appear in Studia Mathematica

References in corpus (3)

• Local smoothing and Hardy spaces for Fourier integral operators
• Rough pseudodifferential operators on Hardy spaces for Fourier integral operators II
• $L^p$ estimates for wave equations with specific $C^{0,1}$ coefficients

Cited by in corpus (4)

• Nonlinear wave equations with slowly decaying initial data
• $L^p$ and ${\mathcal{H}}_{FIO}^p$ regularity for wave equations with rough coefficients
• Local smoothing and Hardy spaces for Fourier integral operators on manifolds
• Function spaces for decoupling