{"paper":{"title":"Ces\\`aro-type operators on mixed norm spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alejandro Mas, \\'Oscar Blasco","submitted_at":"2025-07-28T07:45:19Z","abstract_excerpt":"Given a positive Borel measure $\\mu$ on $[0,1)$ and a parameter $\\beta>0$, we consider the Ces\\`aro-type operator $\\mathcal C_{\\mu,\\beta}$ acting on the analytic function $f(z)=\\sum_{n=0}^\\infty a_n z^n$ on the unit disc of the complex plane $\\mathbb D$, defined by \\[ \\mathcal C_{\\mu,\\beta}(f)(z)= \\sum_{n=0}^\\infty \\mu_n \\left( \\sum_{k=0}^n \\frac{\\Gamma(n-k+\\beta)}{(n-k)! \\Gamma(\\beta)} a_k \\right) z^n = \\int_0^1 \\frac{f(tz)}{(1-tz)^\\beta} d\\mu(t), \\] where $\\mu_n=\\int_0^1 t^n d\\mu(t)$. This operator generalizes the classical Ces\\`aro operator (corresponding to the case where $\\mu$ is the Lebe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20586","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.20586/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}