{"paper":{"title":"Hardy-Littlewood Maximal Operator And $BLO^{1/\\log}$ Class of Exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Shalva Zviadadze, Tengiz Kopaliani","submitted_at":"2014-12-21T15:13:17Z","abstract_excerpt":"It is well known that if Hardy-Littlewood maximal operator is bounded in space $L^{p(\\cdot)}[0;1]$ then $1/p(\\cdot)\\in BMO^{1/\\log}$. On the other hand if $p(\\cdot)\\in BMO^{1/\\log},$ ($1<p_{-}\\leq p_{+}<\\infty$), then there exists $c>0$ such that Hardy-Littlewood maximal operator is bounded in $L^{p(\\cdot)+c}[0;1].$ Also There exists exponent $p(\\cdot)\\in BMO^{1/\\log},$ ($1<p_{-}\\leq p_{+}<\\infty$) such that Hardy-Littlewood maximal operator is not bounded in $L^{p(\\cdot)}[0;1]$. In the present paper we construct exponent $p(\\cdot),$ $(1<p_{-}\\leq p_{+}<\\infty)$, $1/p(\\cdot)\\in BLO^{1/\\log}$ s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6795","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"}