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This answers one of Maz'ya's questions from a collection of 75 open problems in analysis."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We construct a translation-invariant Banach space of locally integrable functions on which M^diamond is bounded, but the sharp maximal operator M^sharp is not.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The space constructed in the paper is a genuine Banach space that is translation-invariant and the boundedness claims for the two operators hold under the definitions given by Maz'ya and Shaposhnikova (abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A translation-invariant Banach space is constructed on which the non-classical maximal operator M^diamond is bounded but the sharp maximal operator M^sharp is not.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"There exists a translation-invariant Banach space of locally integrable functions on which M^diamond is bounded but the sharp maximal operator M^sharp is not.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cbd52e850dc508a558ed84aa8dac7c9ce6d294462c874167062947607e8fb409"},"source":{"id":"2605.17663","kind":"arxiv","version":1},"verdict":{"id":"594f8bc7-8077-44b2-bd57-e0202cbc2574","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:02:48.697875Z","strongest_claim":"We construct a translation-invariant Banach space of locally integrable functions on which M^diamond is bounded, but the sharp maximal operator M^sharp is not.","one_line_summary":"A translation-invariant Banach space is constructed on which the non-classical maximal operator M^diamond is bounded but the sharp maximal operator M^sharp is not.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The space constructed in the paper is a genuine Banach space that is translation-invariant and the boundedness claims for the two operators hold under the definitions given by Maz'ya and Shaposhnikova (abstract).","pith_extraction_headline":"There exists a translation-invariant Banach space of locally integrable functions on which M^diamond is bounded but the sharp maximal operator M^sharp is not."},"integrity":{"clean":false,"summary":{"advisory":1,"critical":0,"by_detector":{"doi_compliance":{"total":1,"advisory":1,"critical":0,"informational":0}},"informational":0},"endpoint":"/pith/2605.17663/integrity.json","findings":[{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. 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