{"paper":{"title":"Mixed norm estimates for the Ces\\`aro means associated with Dunkl--Hermite expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"L. Roncal, Pradeep Boggarapu, S. Thangavelu","submitted_at":"2014-10-08T15:21:38Z","abstract_excerpt":"Our main goal in this article is to study mixed norm estimates for the Ces\\`{a}ro means associated with Dunkl--Hermite expansions on $\\mathbb{R}^d$. These expansions arise when one consider the Dunkl--Hermite operator (or Dunkl harmonic oscillator) $H_{\\kappa}:=-\\Delta_{\\kappa}+|x|^2$, where $\\Delta_{\\kappa}$ stands for the Dunkl--Laplacian. It is shown that the desired mixed norm estimates are equivalent to vector-valued inequalities for a sequence of Ces\\`{a}ro means for Laguerre expansions with shifted parameter. In order to obtain the latter, we develop an argument to extend these operator"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2162","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"}