{"paper":{"title":"On an Interesting Class of Variable Exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Yu. Karlovich, Ilya M. Spitkovsky","submitted_at":"2011-10-03T08:50:17Z","abstract_excerpt":"Let $\\mathcal{M}(\\mathbb{R}^n)$ be the class of functions $p:\\mathbb{R}^n\\to[1,\\infty]$ bounded away from one and infinity and such that the Hardy-Littlewood maximal function is bounded on the variable Lebesgue space $L^{p(\\cdot)}(\\mathbb{R}^n)$. We denote by $\\mathcal{M}^*(\\mathbb{R}^n)$ the class of variable exponents $p\\in\\mathcal{M}(\\mathbb{R}^n)$ for which $1/p(x)=\\theta/p_0+(1-\\theta)/p_1(x)$ with some $p_0\\in(1,\\infty)$, $\\theta\\in(0,1)$, and $p_1\\in\\mathcal{M}(\\mathbb{R}^n)$. Rabinovich and Samko \\cite{RS08} observed that each globally log-H\\\"older continuous exponent belongs to $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0299","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"}