{"paper":{"title":"Some new iterated hardy-type inequalities: The case $\\theta = 1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Amiran Gogatishvili, Lars-Erik Persson, Rza Chingiz Mustafayev","submitted_at":"2013-02-14T15:40:22Z","abstract_excerpt":"In this paper we characterize the validity of the Hardy-type inequality \\begin{equation*} \\left\\|\\left\\|\\int_s^{\\infty}h(z)dz\\right\\|_{p,u,(0,t)}\\right\\|_{q,w,\\infty}\\leq c \\,\\|h\\|_{1,v,\\infty} \\end{equation*} where $0<p< \\infty$, $0<q\\leq +\\infty$, $u$, $w$ and $v$ are weight functions on $(0,\\infty)$. It is pointed out that this characterization can be used to obtain new characterizations for the boundedness between weighted Lebesgue spaces for Hardy-type operators restricted to the cone of monotone functions and for the generalized Stieltjes operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3436","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"}