{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YNXW33TNDQFON3S6QN4DV64OOJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1d478223932567de7c3dbc41e8328b8f00c570ac9b60a5d7e1e8bd62810c2240","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-05T05:22:26Z","title_canon_sha256":"50fe06274d6cd2869bee63bea7e736728ed2847ef1b7fa85b371e4ef507976e2"},"schema_version":"1.0","source":{"id":"1907.02680","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02680","created_at":"2026-07-05T03:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02680v3","created_at":"2026-07-05T03:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02680","created_at":"2026-07-05T03:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"YNXW33TNDQFO","created_at":"2026-07-05T03:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"YNXW33TNDQFON3S6","created_at":"2026-07-05T03:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"YNXW33TN","created_at":"2026-07-05T03:11:51Z"}],"graph_snapshots":[{"event_id":"sha256:c36640aa24dd8ae212354e2d8c3a56135abfbecad614e608c3b6ff7585edbd2e","target":"graph","created_at":"2026-07-05T03:11:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1907.02680/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Jan Rozendaal","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-05T05:22:26Z","title":"Characterizations of Hardy spaces for Fourier integral operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02680","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2f6163a0ea0cadc6b17aa39d1de2398766fb8d0f17480d3042a004501978f416","target":"record","created_at":"2026-07-05T03:11:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1d478223932567de7c3dbc41e8328b8f00c570ac9b60a5d7e1e8bd62810c2240","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-05T05:22:26Z","title_canon_sha256":"50fe06274d6cd2869bee63bea7e736728ed2847ef1b7fa85b371e4ef507976e2"},"schema_version":"1.0","source":{"id":"1907.02680","kind":"arxiv","version":3}},"canonical_sha256":"c36f6dee6d1c0ae6ee5e83783afb8e726e4042301c8fb2be60bc1f7311b49ef9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c36f6dee6d1c0ae6ee5e83783afb8e726e4042301c8fb2be60bc1f7311b49ef9","first_computed_at":"2026-07-05T03:11:51.558271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:11:51.558271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jilA0f7SA7JE/3koXq0kw5eNnhjphOo93R3P8fzKu97LZ80ZSLuspqUxye9aMYDqQ5z7yhnPf0v38ln1KHhhCA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:11:51.558702Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.02680","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f6163a0ea0cadc6b17aa39d1de2398766fb8d0f17480d3042a004501978f416","sha256:c36640aa24dd8ae212354e2d8c3a56135abfbecad614e608c3b6ff7585edbd2e"],"state_sha256":"bc774f4250f79fc2c7d69a461b9d7586094ad04d3157f9eddbb7e0e25f7ec9dc"}