{"paper":{"title":"Quasi-extremals for convolution with surface measure on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Betsy Stovall","submitted_at":"2017-10-23T14:36:42Z","abstract_excerpt":"If $T$ is the operator given by convolution with surface measure on the sphere, $(E,F)$ is a quasi-extremal pair of sets for $T$ if $\\langle T\\chi_E, \\chi_F \\rangle \\gtrsim |E|^{d/(d+1)}|F|^{d/(d+1)}$. In this article, we explicitly define a family $\\mathcal{F}$ of quasi-extremal pairs of sets for $T$. We prove that $\\mathcal{F}$ is fundamental in the sense that every quasi-extremal pair $(E,F)$ is comparable (in a rather strong sense) to a pair from $\\mathcal{F}$. This extends work carried out by M. Christ for convolution with surface measure on the paraboloid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08304","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"}