{"paper":{"title":"Analysis related to all admissible type parameters in the Jacobi setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Adam Nowak, Peter Sj\\\"ogren, Tomasz Z. Szarek","submitted_at":"2012-11-14T10:54:57Z","abstract_excerpt":"We derive an integral representation for the Jacobi-Poisson kernel valid for all admissible type parameters $\\alpha,\\beta$ in the context of Jacobi expansions. This enables us to develop a technique for proving standard estimates in the Jacobi setting, which works for all possible $\\alpha$ and $\\beta$. As a consequence, we can prove that several fundamental operators in the harmonic analysis of Jacobi expansions are (vector-valued) Calder\\'on-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory. The new Ja"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3270","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"}