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We give sufficient conditions on a bounded continuous function m(v) which guarantee that the operator H(m Hf) is bounded on L^p(d\\nu) and of weak-type (1,1), or bounded on the Hardy space H^1((0,infty)^d, d\\nu) in the sense of Coifman-Weiss."},"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":"1110.2348","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-11T12:30:02Z","cross_cats_sorted":[],"title_canon_sha256":"bf1b67906b25bfb38fa77c8e8beb3eefed814c96a2d4fe846b94cd39457056cc","abstract_canon_sha256":"6afd8a81be9a49fe2950e0747d34ae31be9c45efc9ced9a8ae9a20ec2955b3e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:07.541508Z","signature_b64":"yXBHbL19iHrtc9eek7hhNPuckE4CIAWPCzn6QiJy68RoVoiEStxEyO3ct3J3LtQvxgzQIkJp1sYApfCmGMmeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca090bd950e95c87a5de5fb5c5c326c2a21768e13d2e56bd74db3533ceb80399","last_reissued_at":"2026-05-18T04:06:07.541001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:07.541001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multivariate H\\\"ormander-type multiplier theorem for the Hankel transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B{\\l}a\\.zej Wr\\'obel, Jacek Dziuba\\'nski, Marcin Preisner","submitted_at":"2011-10-11T12:30:02Z","abstract_excerpt":"Let H(f)(x)=\\int_{(0,infty)^d} f(v) E_{x}(v) d\\nu(v), be the multivariable Hankel transform, where E_{x}(v)=\\prod_{k=1}^d (x_k v_k)^{-a_k+1/2} J_{a_k-1/2}(x_k v_k), d\\nu(v)=v^a dv, a=(a_1,...,a_d). We give sufficient conditions on a bounded continuous function m(v) which guarantee that the operator H(m Hf) is bounded on L^p(d\\nu) and of weak-type (1,1), or bounded on the Hardy space H^1((0,infty)^d, d\\nu) in the sense of Coifman-Weiss."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2348","kind":"arxiv","version":2},"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":"1110.2348","created_at":"2026-05-18T04:06:07.541075+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.2348v2","created_at":"2026-05-18T04:06:07.541075+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2348","created_at":"2026-05-18T04:06:07.541075+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZIEQXWKQ5FOI","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZIEQXWKQ5FOIPJO6","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZIEQXWKQ","created_at":"2026-05-18T12:26:47.523578+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/ZIEQXWKQ5FOIPJO6L624LQZGYK","json":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK.json","graph_json":"https://pith.science/api/pith-number/ZIEQXWKQ5FOIPJO6L624LQZGYK/graph.json","events_json":"https://pith.science/api/pith-number/ZIEQXWKQ5FOIPJO6L624LQZGYK/events.json","paper":"https://pith.science/paper/ZIEQXWKQ"},"agent_actions":{"view_html":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK","download_json":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK.json","view_paper":"https://pith.science/paper/ZIEQXWKQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.2348&json=true","fetch_graph":"https://pith.science/api/pith-number/ZIEQXWKQ5FOIPJO6L624LQZGYK/graph.json","fetch_events":"https://pith.science/api/pith-number/ZIEQXWKQ5FOIPJO6L624LQZGYK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK/action/storage_attestation","attest_author":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK/action/author_attestation","sign_citation":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK/action/citation_signature","submit_replication":"https://pith.science/pith/ZIEQXWKQ5FOIPJO6L624LQZGYK/action/replication_record"}},"created_at":"2026-05-18T04:06:07.541075+00:00","updated_at":"2026-05-18T04:06:07.541075+00:00"}