{"paper":{"title":"Characterizations of Hardy spaces for Fourier integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Jan Rozendaal","submitted_at":"2019-07-05T05:22:26Z","abstract_excerpt":"We prove several characterizations of the Hardy spaces for Fourier integral operators $\\mathcal{H}^{p}_{FIO}(\\mathbb{R}^{n})$, for $1<p<\\infty$. First we characterize $\\mathcal{H}^{p}_{FIO}(\\mathbb{R}^{n})$ in terms of $L^{p}(\\mathbb{R}^{n})$-norms of parabolic frequency localizations. As a corollary, any characterization of $L^{p}(\\mathbb{R}^{n})$ yields a corresponding version for $\\mathcal{H}^{p}_{FIO}(\\mathbb{R}^{n})$. In particular, we obtain a maximal function characterization and a characterization in terms of vertical square functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02680","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.02680/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}