The Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ for Fourier integral operators for $p<1$
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| Format: | Preprint |
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2025
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| _version_ | 1866909741519732736 |
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| author | Liu, Naijia Rozendaal, Jan Song, Liang |
| author_facet | Liu, Naijia Rozendaal, Jan Song, Liang |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_13243 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ for Fourier integral operators for $p<1$ Liu, Naijia Rozendaal, Jan Song, Liang Analysis of PDEs Classical Analysis and ODEs Primary 42B35. Secondary 35S30, 42B30, 42B37 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. |
| title | The Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ for Fourier integral operators for $p<1$ |
| topic | Analysis of PDEs Classical Analysis and ODEs Primary 42B35. Secondary 35S30, 42B30, 42B37 |
| url | https://arxiv.org/abs/2508.13243 |