{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JA2X6BU3S6UEFDU22TKYTFWHOQ","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":"afcb010ee8d59df9157c25738b77bd047a37e8d2a6f51a4fefcb20ff18a38c9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-23T01:56:47Z","title_canon_sha256":"4992e83fe4b6d063b3a664e470fc41d11085db07e137aee5a6b4f59919634989"},"schema_version":"1.0","source":{"id":"1710.08061","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08061","created_at":"2026-05-18T00:32:19Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08061v1","created_at":"2026-05-18T00:32:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08061","created_at":"2026-05-18T00:32:19Z"},{"alias_kind":"pith_short_12","alias_value":"JA2X6BU3S6UE","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"JA2X6BU3S6UEFDU2","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"JA2X6BU3","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:bf3987562b94e6c64c4bd2457014680787486e7372c0fa23a33a61d8a8c428d8","target":"graph","created_at":"2026-05-18T00:32:19Z","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"},"paper":{"abstract_excerpt":"Let $n\\ge 2$ be the spatial dimension. The purpose of this note is to obtain some weighted estimates for the fractional maximal operator ${\\mathfrak M}{\\alpha}$ of order $\\alpha$, $0\\le\\alpha<n$, on the weighted Choquet-Lorentz space $L^{p,q}(H_{w}^{d})$, where the weight $w$ is arbitrary and the underlying measure is the weighted $d$-dimensional Hausdorff content $H^{d}_{w}$, $0<d\\le n$. Concerning a dependence of two parameters $\\alpha$ and $d$, we establish a general form of the Fefferman-Stein type inequalities for ${\\mathfrak M}_{\\alpha}$. Our results contain the works of Adams, \\cite{Ad}","authors_text":"Hiroki Saito, Hitoshi Tanaka, Toshikazu Watanabe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-23T01:56:47Z","title":"Fractional maximal operators with weighted Hausdorff content"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08061","kind":"arxiv","version":1},"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:afbe3f7af467e6e80da7e183e22cf017c9259a98ea70d6ecbf0ced88e2f51c38","target":"record","created_at":"2026-05-18T00:32:19Z","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":"afcb010ee8d59df9157c25738b77bd047a37e8d2a6f51a4fefcb20ff18a38c9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-23T01:56:47Z","title_canon_sha256":"4992e83fe4b6d063b3a664e470fc41d11085db07e137aee5a6b4f59919634989"},"schema_version":"1.0","source":{"id":"1710.08061","kind":"arxiv","version":1}},"canonical_sha256":"48357f069b97a8428e9ad4d58996c7743270d5c97746045f36c7f5ddc0b6b1c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48357f069b97a8428e9ad4d58996c7743270d5c97746045f36c7f5ddc0b6b1c3","first_computed_at":"2026-05-18T00:32:19.100547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:19.100547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z8llShlWWM3RdPsxUAFExOCDEf9gSi3DvZr/w9IJKlxFHg4GAImv7s4lyeI6Qk3E2fbLIE1JIDYRc6zsSxhOCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:19.100928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.08061","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afbe3f7af467e6e80da7e183e22cf017c9259a98ea70d6ecbf0ced88e2f51c38","sha256:bf3987562b94e6c64c4bd2457014680787486e7372c0fa23a33a61d8a8c428d8"],"state_sha256":"5cb37519938c9b21e691b00e33366c57e568e2c32ed0c487b9b366aa0c037687"}