{"paper":{"title":"On singular integral operators with semi-almost periodic coefficients on variable Lebesgue spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexei Yu. Karlovich, Ilya M. Spitkovsky","submitted_at":"2011-05-02T19:09:32Z","abstract_excerpt":"Let $a$ be a semi-almost periodic matrix function with the almost periodic representatives $a_l$ and $a_r$ at $-\\infty$ and $+\\infty$, respectively. Suppose $p:\\mathbb{R}\\to(1,\\infty)$ is a slowly oscillating exponent such that the Cauchy singular integral operator $S$ is bounded on the variable Lebesgue space $L^{p(\\cdot)}(\\mathbb{R})$. We prove that if the operator $aP+Q$ with $P=(I+S)/2$ and $Q=(I-S)/2$ is Fredholm on the variable Lebesgue space $L_N^{p(\\cdot)}(\\mathbb{R})$, then the operators $a_lP+Q$ and $a_rP+Q$ are invertible on standard Lebesgue spaces $L_N^{q_l}(\\mathbb{R})$ and $L_N^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0407","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"}