{"paper":{"title":"Optimal relations between Lp-norms for the Hardy operator and its dual","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Viktor Kolyada","submitted_at":"2012-06-08T11:22:41Z","abstract_excerpt":"We obtain sharp two-sided inequalities between $L^p-$norms $(1<p<\\infty)$ of functions $Hf$ and $H^*f$, where $H$ is the Hardy operator, $H^*$ is its dual, and $f$ is a nonnegative measurable function on $(0,\\infty).$ In an equivalent form, it gives sharp constants in the two-sided relations between $L^p$-norms of functions $H\\f-\\f$ and $\\f$, where $\\f$ is a nonnegative nonincreasing function on $(0,+\\infty)$ with $\\f(+\\infty)=0.$ In particular, it provides an alternative proof of a result obtained by N. Kruglyak and E. Setterqvist (2008) for $p=2k (k\\in \\N)$ and by S. Boza and J. Soria (2011)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1731","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"}