{"paper":{"title":"Some aspects of harmonic analysis related to Gegenbauer expansions on the half-line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Elman J. Ibrahimov, Vagif S. Guliyev","submitted_at":"2013-10-25T08:48:54Z","abstract_excerpt":"In this paper we consider the generalized shift operator, generated by the Gegenbauer differential operator $$ G =\\left(x^2-1\\right)^{\\frac{1}{2}-\\lambda} \\frac{d}{dx} \\left(x^2-1\\right)^{\\lambda+\\frac{1}{2}}\\frac{d}{dx}. $$ Maximal function ($ G- $ maximal function), generated by the Gegenbauer differential operator $ G $ is investigated. The $ L_{p,\\lambda} $ -boundedness for the $ G- $ maximal function is obtained. The concept of potential of Riesz-Gegenbauer is introduced and for it the theorem of Sobolev type is proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6852","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"}