{"paper":{"title":"Multi-parameter singular Radon transforms III: real analytic surfaces","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":"2011-05-23T19:31:25Z","abstract_excerpt":"The goal of this paper is to study operators of the form, \\[ Tf(x)= \\psi(x)\\int f(\\gamma_t(x))K(t)\\: dt, \\] where $\\gamma$ is a real analytic 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 cutoff function supported near $0\\in \\R^n$, and $K$ is a \"multi-parameter singular kernel\" supported near $0\\in \\R^N$. A main example is when $K$ is a \"product kernel.\" We also study maximal operators of the form, \\[ \\mathcal{M} f(x) = \\psi(x)\\sup_{0<\\delta_1,..., \\delta_N<<1} \\int_{|t|<1} |f(\\gamma_{\\delta_1 t_1,...,\\delta_N t_N}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4589","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"}