{"paper":{"title":"A proof of the Bochner-Riesz conjecture","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Yong-Cheol Kim","submitted_at":"2004-07-01T07:11:08Z","abstract_excerpt":"For $f\\in {\\frak S}({\\Bbb R}^d)$, we consider the Bochner-Riesz operator ${\\frak R}^{\\delta}$ of index $\\delta>0$ defined by $$\\hat {{\\frak R}^{\\delta}f}(\\xi)=(1-|\\xi|^2)^{\\delta}_+ \\hat f (\\xi).$$ Then we prove the Bochner-Riesz conjecture which states that if $\\delta>\\max\\{d|1/p-1/2|-1/2,0\\}$ and $p>1$ then ${\\frak R}^{\\delta}$ is a bounded operator from $L^p({\\Bbb R}^d)$ into $L^p({\\Bbb R}^d)$; moreover, if $\\delta(p)=d(1/p-1/2)-1/2$ and $1<p<2d/(d+1)$, then ${\\frak R}^{\\delta(p)}$ is a bounded operator from $L^p({\\Bbb R}^d)$ into $L^{p,\\infty}({\\Bbb R}^d)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407013","kind":"arxiv","version":4},"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"}