{"paper":{"title":"Discrete analogues in harmonic analysis: Spherical averages","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Magyar, E. M. Stein, S. Wainger","submitted_at":"2004-09-20T17:39:49Z","abstract_excerpt":"In this paper we prove an analogue in the discrete setting of \\Bbb Z^d, of the spherical maximal theorem for \\Bbb R^d. The methods used are two-fold: the application of certain \"sampling\" techniques, and ideas arising in the study of the number of representations of an integer as a sum of d squares in particular, the \"circle method\". The results we obtained are by necessity limited to d \\ge 5, and moreover the range of p for the L^p estimates differs from its analogue in \\Bbb R^d."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409365","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/math/0409365/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"}