{"paper":{"title":"Some $s$-numbers of an integral operator of Hardy type in Banach function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Amiran Gogatishvili, David Edmunds, Nino Samashvili, Tengiz Kopaliani","submitted_at":"2015-07-31T12:29:50Z","abstract_excerpt":"Let $s_{n}(T)$ denote the $n$th approximation, isomorphism, Gelfand, Kolmogorov or Bernstein number of the Hardy-type integral operator $T$ given by\n  $$\n  Tf(x)=v(x)\\int_{a}^{x}u(t)f(t)dt,\\,\\,\\,x\\in(a,b)\\,\\,(-\\infty<a<b<+\\infty)\n  $$\n  and mapping a Banach function space $E$ to itself. We investigate some geometrical properties of $E$ for which\n  $$ C_{1}\\int_{a}^{b}u(x)v(x)dx \\leq\\limsup\\limits_{n\\rightarrow\\infty}ns_{n}(T)\n  \\leq \\limsup\\limits_{n\\rightarrow\\infty}ns_{n}(T)\\leq C_{2}\\int_{a}^{b}u(x)v(x)dx $$ under appropriate conditions on $u$ and $v.$ The constants $C_{1},C_{2}>0$ depend o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08854","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"}