{"paper":{"title":"Endpoint Sobolev and BV Continuity for maximal operators, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jos\\'e Madrid","submitted_at":"2017-10-10T12:49:30Z","abstract_excerpt":"In this paper we study some questions about the continuity of classical and fractional maximal operators in the Sobolev space $W^{1,1}$, in both continuous and discrete setting, giving a positive answer to two questions posed recently, one of them regarding the continuity of the map $f \\mapsto \\big(\\widetilde M_{\\beta}f\\big)'$ from $W^{1,1}(\\mathbb{R})$ to $L^q(\\mathbb{R})$, for $q=\\frac{1}{1-\\beta}$. Here $\\widetilde M_{\\beta}$ denotes the non-centered fractional maximal operator on $\\mathbb{R}$ with $\\beta\\in(0,1)$. The second one regarding the continuity of the discrete centered maximal ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03546","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"}