{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:DWMQXNTI4LATEGOP57UJZ4WRSL","short_pith_number":"pith:DWMQXNTI","schema_version":"1.0","canonical_sha256":"1d990bb668e2c13219cfefe89cf2d192f6b86e1fbef9d3859bd05f33ccfd8513","source":{"kind":"arxiv","id":"2502.03151","version":1},"attestation_state":"computed","paper":{"title":"$L^p$-estimates for the 2D wave equation in the scaling-critical magnetic field","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fang Zhang, Jialu Wang, Jiqiang Zheng, Junyong Zhang","submitted_at":"2025-02-05T13:22:37Z","abstract_excerpt":"In this paper, we study the $L^{p}$-estimates for the solution to the $2\\mathrm{D}$-wave equation with a scaling-critical magnetic potential. Inspired by the work of \\cite{FZZ}, we show that the operators $(I+\\mathcal{L}_{\\mathbf{A}})^{-\\gamma}e^{it\\sqrt{\\mathcal{L}_{\\mathbf{A}}}}$ is bounded in $L^{p}(\\mathbb{R}^{2})$ for $1<p<+\\infty$ when $\\gamma>|1/p-1/2|$ and $t>0$, where $\\mathcal{L}_{\\mathbf{A}}$ is a magnetic Schr\\\"odinger operator. In particular, we derive the $L^{p}$-bounds for the sine wave propagator $\\sin(t\\sqrt{\\mathcal{L}_{\\mathbf{A}}})\\mathcal{L}^{-\\frac12}_{\\mathbf{A}}$. The k"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2502.03151","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-02-05T13:22:37Z","cross_cats_sorted":[],"title_canon_sha256":"051163092082c1285d6698f35150ccb8e1bde8c8855c922981852f36eb54388f","abstract_canon_sha256":"8decc56f2887e516a40ad54aad9a6fa9e21dc30000079fae5744585fd602eeb5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:10:00.539464Z","signature_b64":"9FZ0DG7qbrLmVqA4ki9sMR+aoCoDkUOWUtwNeD3XWjR7grkmigqtQ1lyYjA/PLa/2haNOJrwi/plvkS8Mkv6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d990bb668e2c13219cfefe89cf2d192f6b86e1fbef9d3859bd05f33ccfd8513","last_reissued_at":"2026-07-05T10:10:00.539098Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:10:00.539098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$L^p$-estimates for the 2D wave equation in the scaling-critical magnetic field","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fang Zhang, Jialu Wang, Jiqiang Zheng, Junyong Zhang","submitted_at":"2025-02-05T13:22:37Z","abstract_excerpt":"In this paper, we study the $L^{p}$-estimates for the solution to the $2\\mathrm{D}$-wave equation with a scaling-critical magnetic potential. Inspired by the work of \\cite{FZZ}, we show that the operators $(I+\\mathcal{L}_{\\mathbf{A}})^{-\\gamma}e^{it\\sqrt{\\mathcal{L}_{\\mathbf{A}}}}$ is bounded in $L^{p}(\\mathbb{R}^{2})$ for $1<p<+\\infty$ when $\\gamma>|1/p-1/2|$ and $t>0$, where $\\mathcal{L}_{\\mathbf{A}}$ is a magnetic Schr\\\"odinger operator. In particular, we derive the $L^{p}$-bounds for the sine wave propagator $\\sin(t\\sqrt{\\mathcal{L}_{\\mathbf{A}}})\\mathcal{L}^{-\\frac12}_{\\mathbf{A}}$. The k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.03151","kind":"arxiv","version":1},"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/2502.03151/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2502.03151","created_at":"2026-07-05T10:10:00.539154+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.03151v1","created_at":"2026-07-05T10:10:00.539154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.03151","created_at":"2026-07-05T10:10:00.539154+00:00"},{"alias_kind":"pith_short_12","alias_value":"DWMQXNTI4LAT","created_at":"2026-07-05T10:10:00.539154+00:00"},{"alias_kind":"pith_short_16","alias_value":"DWMQXNTI4LATEGOP","created_at":"2026-07-05T10:10:00.539154+00:00"},{"alias_kind":"pith_short_8","alias_value":"DWMQXNTI","created_at":"2026-07-05T10:10:00.539154+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DWMQXNTI4LATEGOP57UJZ4WRSL","json":"https://pith.science/pith/DWMQXNTI4LATEGOP57UJZ4WRSL.json","graph_json":"https://pith.science/api/pith-number/DWMQXNTI4LATEGOP57UJZ4WRSL/graph.json","events_json":"https://pith.science/api/pith-number/DWMQXNTI4LATEGOP57UJZ4WRSL/events.json","paper":"https://pith.science/paper/DWMQXNTI"},"agent_actions":{"view_html":"https://pith.science/pith/DWMQXNTI4LATEGOP57UJZ4WRSL","download_json":"https://pith.science/pith/DWMQXNTI4LATEGOP57UJZ4WRSL.json","view_paper":"https://pith.science/paper/DWMQXNTI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.03151&json=true","fetch_graph":"https://pith.science/api/pith-number/DWMQXNTI4LATEGOP57UJZ4WRSL/graph.json","fetch_events":"https://pith.science/api/pith-number/DWMQXNTI4LATEGOP57UJZ4WRSL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DWMQXNTI4LATEGOP57UJZ4WRSL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DWMQXNTI4LATEGOP57UJZ4WRSL/action/storage_attestation","attest_author":"https://pith.science/pith/DWMQXNTI4LATEGOP57UJZ4WRSL/action/author_attestation","sign_citation":"https://pith.science/pith/DWMQXNTI4LATEGOP57UJZ4WRSL/action/citation_signature","submit_replication":"https://pith.science/pith/DWMQXNTI4LATEGOP57UJZ4WRSL/action/replication_record"}},"created_at":"2026-07-05T10:10:00.539154+00:00","updated_at":"2026-07-05T10:10:00.539154+00:00"}