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arXiv · 2508.13243

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

Naijia Liu·Jan Rozendaal·Liang Song
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Abstract

We introduce the Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ for Fourier integral operators for $0<p<1$, thereby extending earlier constructions for $1\leq p\leq \infty$. We then establish various properties of these spaces, including their behavior under complex interpolation and duality, and their invariance under Fourier integral operators. We also obtain Sobolev embeddings, equivalent characterizations, and a molecular decomposition. These spaces are used in the companion article arXiv:2502.02511 to determine the sharp $\mathcal{H}^{1}(\mathbb{R}^{n})$ and $\mathrm{bmo}(\mathbb{R}^{n})$ regularity of wave equations with rough coefficients.

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Naijia Liu, Jan Rozendaal, Liang Song. 2025-08-18. The Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ for Fourier integral operators for $p<1$. https://arxiv.org/abs/2508.13243

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