{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FZHEYHPB25AULUSC2YMLQ2ALHR","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":"dbf8a089fcabe519e245d3e92bac1d36f53e03a48002bf6fa760b6457d23bb46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-01-06T20:41:33Z","title_canon_sha256":"3fe18f2762e145306afcffb2282a3533542816bebe9f65c89a1894297f2941f7"},"schema_version":"1.0","source":{"id":"1301.1051","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1051","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1051v2","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1051","created_at":"2026-05-18T03:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"FZHEYHPB25AU","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FZHEYHPB25AULUSC","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FZHEYHPB","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:df4cfaa801a87231668fe92b8f317b2ab3ce8ece05b99af85e376e0868555a56","target":"graph","created_at":"2026-05-18T03:36:06Z","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 $S_{\\a,\\psi}(f)$ be the square function defined by means of the cone in ${\\mathbb R}^{n+1}_{+}$ of aperture $\\a$, and a standard kernel $\\psi$. Let $[w]_{A_p}$ denote the $A_p$ characteristic of the weight $w$. We show that for any $1<p<\\infty$ and $\\a\\ge 1$, $$\\|S_{\\a,\\psi}\\|_{L^p(w)}\\lesssim \\a^n[w]_{A_p}^{\\max(1/2,\\frac{1}{p-1})}.$$ For each fixed $\\a$ the dependence on $[w]_{A_p}$ is sharp. Also, on all class $A_p$ the result is sharp in $\\a$. Previously this estimate was proved in the case $\\a=1$ using the intrinsic square function. However, that approach does not allow to get the abo","authors_text":"Andrei K. Lerner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-01-06T20:41:33Z","title":"On sharp aperture-weighted estimates for square functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1051","kind":"arxiv","version":2},"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:f7df8bd60faa2fa136f276ba0b17348e162ba7d1838e2241a8b35dd7e3af1f97","target":"record","created_at":"2026-05-18T03:36:06Z","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":"dbf8a089fcabe519e245d3e92bac1d36f53e03a48002bf6fa760b6457d23bb46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-01-06T20:41:33Z","title_canon_sha256":"3fe18f2762e145306afcffb2282a3533542816bebe9f65c89a1894297f2941f7"},"schema_version":"1.0","source":{"id":"1301.1051","kind":"arxiv","version":2}},"canonical_sha256":"2e4e4c1de1d74145d242d618b8680b3c5cd2146eb928fa2eda38082ab98eb4e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e4e4c1de1d74145d242d618b8680b3c5cd2146eb928fa2eda38082ab98eb4e3","first_computed_at":"2026-05-18T03:36:06.012923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:06.012923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4zCXDBynukuxTgMpHVnZUiPvHzR0V8H2ebh3OXFNy08ipi/lM2Ji6dPVan1JcwqAybx5Cfu/LneQ7aElvkd0Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:06.013708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1051","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7df8bd60faa2fa136f276ba0b17348e162ba7d1838e2241a8b35dd7e3af1f97","sha256:df4cfaa801a87231668fe92b8f317b2ab3ce8ece05b99af85e376e0868555a56"],"state_sha256":"afe1dcafad1eeb7391f45408bb12966d741cadcd46aa5f7180e3390c65c13a27"}