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Betancor, Pablo Quijano","submitted_at":"2025-06-17T15:26:04Z","abstract_excerpt":"In this paper we consider fractional Kolmogorov operators defined, in $\\mathbb{R}^d$, by\n  \\[\\Lambda_\\kappa=(-\\Delta)^{\\alpha/2}+\\frac{\\kappa}{|x|^\\alpha} x\\cdot \\nabla,\\]\n  with $\\alpha\\in (1,2)$, $\\alpha<(d+2)/2$ and $\\kappa\\in \\mathbb{R}$. The operator $\\Lambda_\\alpha$ generates a holomorphic semigroup $\\{T_t^\\alpha\\}_{t>0}$ in $L^2(\\mathbb{R}^d)$ provided that $\\kappa<\\kappa_c$ where $\\kappa_c$ is a critical coupling constant. We establish $L^p$-boundedness properties for the variation operators $V_\\rho\\left(\\{t^\\ell\\partial_t^\\ell T_t^\\alpha\\}_{t>0}\\right)$ with $\\rho> 2$, $\\ell\\in \\mathb"},"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":"2506.14631","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-17T15:26:04Z","cross_cats_sorted":[],"title_canon_sha256":"09787fd46e53f15f9fc7730dc5e1cb35b898b8e09b58a4e179e484147daabc1b","abstract_canon_sha256":"820c296762d074945c142efcff5a128d68d46232a899190f2e2b5f23306df10c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:59.995490Z","signature_b64":"fAyPMX2lA9xejI6GOv2nrPibVuhNhW8w2G+JSd+/kGWA11P3vkL2zZ+O3BwkmLBPh/qIlG7iKXcSJpFzB8s3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29781427c56d82f488e0b0db51a53aeafec1a6b56cd53b317d52d63ae3201842","last_reissued_at":"2026-07-05T11:22:59.994992Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:59.994992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Estefan\\'ia Dalmasso, Jorge J. 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We establish $L^p$-boundedness properties for the variation operators $V_\\rho\\left(\\{t^\\ell\\partial_t^\\ell T_t^\\alpha\\}_{t>0}\\right)$ with $\\rho> 2$, $\\ell\\in \\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.14631","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.14631/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.14631","created_at":"2026-07-05T11:22:59.995058+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.14631v1","created_at":"2026-07-05T11:22:59.995058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.14631","created_at":"2026-07-05T11:22:59.995058+00:00"},{"alias_kind":"pith_short_12","alias_value":"FF4BIJ6FNWBP","created_at":"2026-07-05T11:22:59.995058+00:00"},{"alias_kind":"pith_short_16","alias_value":"FF4BIJ6FNWBPJCHA","created_at":"2026-07-05T11:22:59.995058+00:00"},{"alias_kind":"pith_short_8","alias_value":"FF4BIJ6F","created_at":"2026-07-05T11:22:59.995058+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/FF4BIJ6FNWBPJCHAWDNVDJJ25L","json":"https://pith.science/pith/FF4BIJ6FNWBPJCHAWDNVDJJ25L.json","graph_json":"https://pith.science/api/pith-number/FF4BIJ6FNWBPJCHAWDNVDJJ25L/graph.json","events_json":"https://pith.science/api/pith-number/FF4BIJ6FNWBPJCHAWDNVDJJ25L/events.json","paper":"https://pith.science/paper/FF4BIJ6F"},"agent_actions":{"view_html":"https://pith.science/pith/FF4BIJ6FNWBPJCHAWDNVDJJ25L","download_json":"https://pith.science/pith/FF4BIJ6FNWBPJCHAWDNVDJJ25L.json","view_paper":"https://pith.science/paper/FF4BIJ6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.14631&json=true","fetch_graph":"https://pith.science/api/pith-number/FF4BIJ6FNWBPJCHAWDNVDJJ25L/graph.json","fetch_events":"https://pith.science/api/pith-number/FF4BIJ6FNWBPJCHAWDNVDJJ25L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FF4BIJ6FNWBPJCHAWDNVDJJ25L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FF4BIJ6FNWBPJCHAWDNVDJJ25L/action/storage_attestation","attest_author":"https://pith.science/pith/FF4BIJ6FNWBPJCHAWDNVDJJ25L/action/author_attestation","sign_citation":"https://pith.science/pith/FF4BIJ6FNWBPJCHAWDNVDJJ25L/action/citation_signature","submit_replication":"https://pith.science/pith/FF4BIJ6FNWBPJCHAWDNVDJJ25L/action/replication_record"}},"created_at":"2026-07-05T11:22:59.995058+00:00","updated_at":"2026-07-05T11:22:59.995058+00:00"}