{"paper":{"title":"On Abel summability of Jacobi polynomials series, the Watson Kernel and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Calixto P. Calder\\'on, Wilfredo Urbina","submitted_at":"2012-07-18T23:42:26Z","abstract_excerpt":"In this paper we return to the study of the Watson kernel for the Abel summabilty of Jacobi polynomial series. These estimates have been studied for over more than 30 years. The main innovations are in the techniques used to get the estimates that allow us to handle the case 0<\\alpha as well as -1< \\alpha <0, with essentially the same method; using an integral superposition of Poisson type kernel and Muckenhoupt A_p-weight theory. We consider a generalization of a theorem due to Zygmund in the context to Borel measures. The proofs are therefore different from the ones given in previous papers "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4524","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"}