{"paper":{"title":"Multi-parameter singular Radon transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Brian Street, Elias M. Stein","submitted_at":"2010-12-13T01:26:08Z","abstract_excerpt":"The purpose of this announcement is to describe a development given in a series of forthcoming papers by the authors that concern operators of the form \\[ f\\mapsto \\psi(x) \\int f(\\gamma_t(x)) K(t)\\: dt, \\] where $\\gamma_t(x)=\\gamma(t,x)$ is a $C^\\infty$ function defined on a neighborhood of the origin in $(t,x)\\in \\mathbb{R}^N\\times \\mathbb{R}^n$ satisfying $\\gamma_0(x)\\equiv x$, $K(t)$ is a \"multi-parameter singular kernel\" supported near $t=0$, and $\\psi$ is a cutoff function supported near $x=0$. This note concerns the case when $K$ is a \"product kernel\". The goal is to give conditions on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2610","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"}