{"paper":{"title":"Semi-Fredholmness of weighted singular integral operators with shifts and slowly oscillating data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexei Yu. Karlovich, Amarino B. Lebre, Yuri I. Karlovich","submitted_at":"2017-05-29T15:19:31Z","abstract_excerpt":"Let $\\alpha,\\beta$ be orientation-preserving homeomorphisms of $[0,\\infty]$ onto itself, which have only two fixed points at $0$ and $\\infty$, and whose restrictions to $\\mathbb{R}_+=(0,\\infty)$ are diffeomorphisms, and let $U_\\alpha,U_\\beta$ be the corresponding isometric shift operators on the space $L^p(\\mathbb{R}_+)$ given by $U_\\mu f=(\\mu')^{1/p}(f\\circ\\mu)$ for $\\mu\\in\\{\\alpha,\\beta\\}$. We prove sufficient conditions for the right and left Fredholmness on $L^p(\\mathbb{R}_+)$ of singular integral operators of the form $A_+P_\\gamma^++A_-P_\\gamma^-$, where $P_\\gamma^\\pm=(I\\pm S_\\gamma)/2$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10247","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"}