{"paper":{"title":"Weighted inequalities for iterated Copson integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lubo\\v{s} Pick, Martin K\\v{r}epela","submitted_at":"2018-06-13T09:17:48Z","abstract_excerpt":"We solve a long-standing open problem in theory of weighted inequalities concerning iterated Copson operators. We use a constructive approximation method based on a new discretization principle that is developed here. In result, we characterize all weight functions $w,v,u$ on $(0,\\infty)$ for which there exists a constant $C$ such that the inequality $$ \\left(\\int_0^{\\infty}\\left(\\int_t^\\infty \\left(\\int_s^{\\infty}h(y)\\,\\text{d}y\\right)^mu(s) \\,\\text{d}s\\right)^{\\frac{q}{m}}w(t)\\,\\text{d}t\\right)^{\\frac{1}{q}} \\le C \\left(\\int_0^{\\infty}h(t)^pv(t)\\,\\text{d}t\\right)^{\\frac{1}{p}} $$ holds for e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04909","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"}