{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:STQUPPLGPREQPL7HIOP7IKLFY3","short_pith_number":"pith:STQUPPLG","schema_version":"1.0","canonical_sha256":"94e147bd667c4907afe7439ff42965c6c12c6166a057b05692f1ab07183fcb13","source":{"kind":"arxiv","id":"1510.06321","version":3},"attestation_state":"computed","paper":{"title":"$L^p$-$L^q$ multipliers on locally compact groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.RT","authors_text":"Michael Ruzhansky, Rauan Akylzhanov","submitted_at":"2015-10-19T12:28:29Z","abstract_excerpt":"In this paper we discuss the $L^p$-$L^q$ boundedness of both spectral and Fourier multipliers on general locally compact separable unimodular groups $G$ for the range $1<p\\leq q<\\infty$. We prove a Lizorkin type multiplier theorem for $1<p\\leq q<\\infty$, and then refine it as a H\\\"ormander type multiplier theorem for $1<p\\leq 2\\leq q<\\infty$. In the process, we establish versions of Paley and Hausdorff-Young-Paley inequalities on general locally compact separable unimodular groups. As a consequence of the H\\\"ormander type multiplier theorem we derive a spectral multiplier theorem on general lo"},"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":"1510.06321","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-10-19T12:28:29Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"2e6697bf038ceb1d0b05b8a59b94792743b17dfd2c796fc8b6cecee9355bcfbf","abstract_canon_sha256":"1b282b1dca4e75d29525dc55e6d513b65ca9b8e80a77c47a0cce17ed598ddf44"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:29.473039Z","signature_b64":"gpP5XSYR5x3XKvfcpKWqCKKVHAmSFphyDUyQop9CNQLhiJsqBDBScLCcVXvA1t//t1Oxwrm8ZBymOfWnG75iAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94e147bd667c4907afe7439ff42965c6c12c6166a057b05692f1ab07183fcb13","last_reissued_at":"2026-05-18T00:47:29.472641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:29.472641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$L^p$-$L^q$ multipliers on locally compact groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.RT","authors_text":"Michael Ruzhansky, Rauan Akylzhanov","submitted_at":"2015-10-19T12:28:29Z","abstract_excerpt":"In this paper we discuss the $L^p$-$L^q$ boundedness of both spectral and Fourier multipliers on general locally compact separable unimodular groups $G$ for the range $1<p\\leq q<\\infty$. We prove a Lizorkin type multiplier theorem for $1<p\\leq q<\\infty$, and then refine it as a H\\\"ormander type multiplier theorem for $1<p\\leq 2\\leq q<\\infty$. In the process, we establish versions of Paley and Hausdorff-Young-Paley inequalities on general locally compact separable unimodular groups. As a consequence of the H\\\"ormander type multiplier theorem we derive a spectral multiplier theorem on general lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06321","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":""},"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":"1510.06321","created_at":"2026-05-18T00:47:29.472703+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.06321v3","created_at":"2026-05-18T00:47:29.472703+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06321","created_at":"2026-05-18T00:47:29.472703+00:00"},{"alias_kind":"pith_short_12","alias_value":"STQUPPLGPREQ","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"STQUPPLGPREQPL7H","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"STQUPPLG","created_at":"2026-05-18T12:29:42.218222+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/STQUPPLGPREQPL7HIOP7IKLFY3","json":"https://pith.science/pith/STQUPPLGPREQPL7HIOP7IKLFY3.json","graph_json":"https://pith.science/api/pith-number/STQUPPLGPREQPL7HIOP7IKLFY3/graph.json","events_json":"https://pith.science/api/pith-number/STQUPPLGPREQPL7HIOP7IKLFY3/events.json","paper":"https://pith.science/paper/STQUPPLG"},"agent_actions":{"view_html":"https://pith.science/pith/STQUPPLGPREQPL7HIOP7IKLFY3","download_json":"https://pith.science/pith/STQUPPLGPREQPL7HIOP7IKLFY3.json","view_paper":"https://pith.science/paper/STQUPPLG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.06321&json=true","fetch_graph":"https://pith.science/api/pith-number/STQUPPLGPREQPL7HIOP7IKLFY3/graph.json","fetch_events":"https://pith.science/api/pith-number/STQUPPLGPREQPL7HIOP7IKLFY3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/STQUPPLGPREQPL7HIOP7IKLFY3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/STQUPPLGPREQPL7HIOP7IKLFY3/action/storage_attestation","attest_author":"https://pith.science/pith/STQUPPLGPREQPL7HIOP7IKLFY3/action/author_attestation","sign_citation":"https://pith.science/pith/STQUPPLGPREQPL7HIOP7IKLFY3/action/citation_signature","submit_replication":"https://pith.science/pith/STQUPPLGPREQPL7HIOP7IKLFY3/action/replication_record"}},"created_at":"2026-05-18T00:47:29.472703+00:00","updated_at":"2026-05-18T00:47:29.472703+00:00"}