{"paper":{"title":"Pseudodifferential Operators 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":"2011-10-03T08:31:45Z","abstract_excerpt":"Let $\\mathcal{M}(\\mathbb{R}^n)$ be the class of bounded away from one and infinity functions $p:\\mathbb{R}^n\\to[1,\\infty]$ such that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue space $L^{p(\\cdot)}(\\mathbb{R}^n)$. We show that if $a$ belongs to the H\\\"ormander class $S_{\\rho,\\delta}^{n(\\rho-1)}$ with $0<\\rho\\le 1$, $0\\le\\delta<1$, then the pseudodifferential operator $\\Op(a)$ is bounded on the variable Lebesgue space $L^{p(\\cdot)}(\\R^n)$ provided that $p\\in\\cM(\\R^n)$. Let $\\mathcal{M}^*(\\mathbb{R}^n)$ be the class of variable exponents $p\\in\\mathcal{M}(\\mathbb{R}^n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0297","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"}