{"paper":{"title":"$L^p$-nondegenerate Radon-like operators with vanishing rotational curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Philip T. Gressman","submitted_at":"2013-08-06T19:38:27Z","abstract_excerpt":"We consider the $L^p \\rightarrow L^q$ mapping properties of a model family of Radon-like operators integrating functions over n-dimensional submanifolds of ${\\mathbb R}^{2n}$. It is shown that nonvanishing rotational curvature is never generic when $n \\geq 2$ and is, in fact, impossible for all but finitely many values of $n$. Nevertheless, operators satisfying the same $L^p \\rightarrow L^q$ estimates as the \"nondegenerate\" case (modulo the endpoint) are dense in the model family for all $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1387","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"}