{"paper":{"title":"Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"J. M. Aldaz, J. P\\'erez L\\'azaro","submitted_at":"2006-01-03T14:37:14Z","abstract_excerpt":"We prove that if $f:I\\subset \\Bbb R\\to \\Bbb R$ is of bounded variation, then the noncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\\|DMf\\|_1\\le |Df|(I)$. This allows us obtain, under less regularity, versions of classical inequalities involving derivatives."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601044","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"}