{"paper":{"title":"Spherical maximal operators on radial functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Seeger, James Wright, Stephen Wainger","submitted_at":"1996-01-01T00:00:00Z","abstract_excerpt":"Let $A_tf(x)=\\int f(x+ty)d\\sigma(y)$ denote the spherical means in $\\Bbb R^d$ ($d\\sigma$ is surface measure on $S^{d-1}$, normalized to $1$). We prove sharp estimates for the maximal function $M_E f(x)=\\sup_{t\\in E}|A_tf(x)|$ where $E$ is a fixed set in $\\Bbb R^+$ and $f$ is a {\\it radial} function $\\in L^p(\\Bbb R^d)$. Let $p_d=d/(d-1)$ (the critical exponent of Stein's maximal function). For the cases (i) $p<p_d$, $d\\ge 2$ and (ii) $p=p_d$, $d\\ge 3$, and for $p\\le q\\le\\infty$ we prove necessary and sufficient conditions for $L^p\\to L^{p,q}$ boundedness of the operator $M_E$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9601220","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":""},"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"}