{"paper":{"title":"Multi-parameter singular Radon transforms I: the $L^2$ theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Brian Street","submitted_at":"2010-05-24T19:11:11Z","abstract_excerpt":"The purpose of this paper is to study the $L^2$ boundedness of operators of the form \\[ f\\mapsto \\psi(x) \\int f(\\gamma_t(x)) K(t) dt, \\] where $\\gamma_t(x)$ is a $C^\\infty$ function defined on a neighborhood of the origin in $(t,x)\\in \\R^N\\times \\R^n$, satisfying $\\gamma_0(x)\\equiv x$, $\\psi$ is a $C^\\infty$ cutoff function supported on a small neighborhood of $0\\in \\R^n$, and $K$ is a \"multi-parameter singular kernel\" supported on a small neighborhood of $0\\in \\R^N$. The goal is, given an appropriate class of kernels $K$, to give conditions on $\\gamma$ such that every operator of the above fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4400","kind":"arxiv","version":2},"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"}