{"paper":{"title":"Fredholmness and Index of Simplest Weighted Singular Integral Operators with Two Slowly Oscillating Shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexei Yu. Karlovich","submitted_at":"2014-05-02T10:05:06Z","abstract_excerpt":"Let $\\alpha$ and $\\beta$ be orientation-preserving diffeomorphisms (shifts) of $\\mathbb{R}_+=(0,\\infty)$ onto itself with the only fixed points $0$ and $\\infty$, where the derivatives $\\alpha'$ and $\\beta'$ may have discontinuities of slowly oscillating type at $0$ and $\\infty$. For $p\\in(1,\\infty)$, we consider the weighted shift operators $U_\\alpha$ and $U_\\beta$ given on the Lebesgue space $L^p(\\mathbb{R}_+)$ by $U_\\alpha f=(\\alpha')^{1/p}(f\\circ\\alpha)$ and $U_\\beta f= (\\beta')^{1/p}(f\\circ\\beta)$. For $i,j\\in\\mathbb{Z}$ we study the simplest weighted singular integral operators with two s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0368","kind":"arxiv","version":3},"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"}