{"paper":{"title":"Maximal inequalities for derivatives of spherical means","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mateusz Kwa\\'snicki","submitted_at":"2026-06-01T23:07:56Z","abstract_excerpt":"We give an alternative formulation of Stein's maximal inequality for generalised spherical averages in terms of derivatives of standard spherical means: if \\[ k \\ge 0, \\qquad d \\ge 2 k + 3 , \\qquad \\frac{d}{d - k - 1} < p < \\frac{d - 1}{k} , \\] and $\\sigma$ is the normalised surface measure on the unit sphere $\\mathbb S$, then the maximal operator \\[f \\mapsto \\sup_{r > 0} \\, \\biggl\\lvert r^k (\\tfrac{d}{dr})^k \\int_{\\mathbb S} f(\\cdot + r y) \\sigma(dy) \\biggr\\rvert\\] is bounded on $L^p$, with a constant that is independent of the dimension $d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02952","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/2606.02952/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"}