{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6GDQWTXPJN4VYLC5KNNGUQXNXZ","short_pith_number":"pith:6GDQWTXP","schema_version":"1.0","canonical_sha256":"f1870b4eef4b795c2c5d535a6a42edbe5d599828847c2c2c00c1a772d44d3507","source":{"kind":"arxiv","id":"1710.07233","version":1},"attestation_state":"computed","paper":{"title":"The Variation of the Fractional Maximal Function of a Radial Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hannes Luiro, Jos\\'e Madrid","submitted_at":"2017-10-19T16:26:39Z","abstract_excerpt":"In this paper we study the regularity of the non-centered fractional maximal operator $M_{\\beta}$. As the main result, we prove that there exists $C(n,\\beta)$ such that if $q=n/(n-\\beta)$ and $f$ is a radial function, then $\\|DM_{\\beta}f\\|_{L^{q}(\\mathbb{R}^n)}\\leq C(n,\\beta)\\|Df\\|_{L^{1}(\\mathbb{R}^n)}$. The corresponding result was previously known only if $n=1$ or $\\beta=0$. Our proofs are almost free from one-dimensional arguments. Therefore, we believe that the new approach may be very useful when trying to extend the result for all $f\\in W^{1,1}(\\mathbb{R}^n)$."},"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":"1710.07233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-19T16:26:39Z","cross_cats_sorted":[],"title_canon_sha256":"afff953b9f8f2b4f8a6f80880efcd41e2ce391109f23bdd04cadb29e03dcc14d","abstract_canon_sha256":"094c0bee7e0c8b5af5a43e7091ca4a7d81cff8b4eb37f5f917a85b615b9ee5a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:26.473523Z","signature_b64":"M0lk9mXClKdGU1PLC+8Y+o0AQPLlHpy04vRc2YR4FhLfvv+a41tjr+kne/RvY4lITuGgbU3RW3THrqn5skmjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1870b4eef4b795c2c5d535a6a42edbe5d599828847c2c2c00c1a772d44d3507","last_reissued_at":"2026-05-18T00:32:26.472846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:26.472846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Variation of the Fractional Maximal Function of a Radial Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hannes Luiro, Jos\\'e Madrid","submitted_at":"2017-10-19T16:26:39Z","abstract_excerpt":"In this paper we study the regularity of the non-centered fractional maximal operator $M_{\\beta}$. As the main result, we prove that there exists $C(n,\\beta)$ such that if $q=n/(n-\\beta)$ and $f$ is a radial function, then $\\|DM_{\\beta}f\\|_{L^{q}(\\mathbb{R}^n)}\\leq C(n,\\beta)\\|Df\\|_{L^{1}(\\mathbb{R}^n)}$. The corresponding result was previously known only if $n=1$ or $\\beta=0$. Our proofs are almost free from one-dimensional arguments. Therefore, we believe that the new approach may be very useful when trying to extend the result for all $f\\in W^{1,1}(\\mathbb{R}^n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07233","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":""},"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":"1710.07233","created_at":"2026-05-18T00:32:26.472942+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.07233v1","created_at":"2026-05-18T00:32:26.472942+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07233","created_at":"2026-05-18T00:32:26.472942+00:00"},{"alias_kind":"pith_short_12","alias_value":"6GDQWTXPJN4V","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6GDQWTXPJN4VYLC5","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6GDQWTXP","created_at":"2026-05-18T12:31:03.183658+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/6GDQWTXPJN4VYLC5KNNGUQXNXZ","json":"https://pith.science/pith/6GDQWTXPJN4VYLC5KNNGUQXNXZ.json","graph_json":"https://pith.science/api/pith-number/6GDQWTXPJN4VYLC5KNNGUQXNXZ/graph.json","events_json":"https://pith.science/api/pith-number/6GDQWTXPJN4VYLC5KNNGUQXNXZ/events.json","paper":"https://pith.science/paper/6GDQWTXP"},"agent_actions":{"view_html":"https://pith.science/pith/6GDQWTXPJN4VYLC5KNNGUQXNXZ","download_json":"https://pith.science/pith/6GDQWTXPJN4VYLC5KNNGUQXNXZ.json","view_paper":"https://pith.science/paper/6GDQWTXP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.07233&json=true","fetch_graph":"https://pith.science/api/pith-number/6GDQWTXPJN4VYLC5KNNGUQXNXZ/graph.json","fetch_events":"https://pith.science/api/pith-number/6GDQWTXPJN4VYLC5KNNGUQXNXZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6GDQWTXPJN4VYLC5KNNGUQXNXZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6GDQWTXPJN4VYLC5KNNGUQXNXZ/action/storage_attestation","attest_author":"https://pith.science/pith/6GDQWTXPJN4VYLC5KNNGUQXNXZ/action/author_attestation","sign_citation":"https://pith.science/pith/6GDQWTXPJN4VYLC5KNNGUQXNXZ/action/citation_signature","submit_replication":"https://pith.science/pith/6GDQWTXPJN4VYLC5KNNGUQXNXZ/action/replication_record"}},"created_at":"2026-05-18T00:32:26.472942+00:00","updated_at":"2026-05-18T00:32:26.472942+00:00"}