{"paper":{"title":"A.e. convergence and 2-weight inequalities for Poisson-Laguerre semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Beatriz Viviani, Gustavo Garrigos, Silvia Hartzstein, Teresa Signes","submitted_at":"2015-11-12T16:59:40Z","abstract_excerpt":"We find optimal decay estimates for the Poisson kernels associated with various Laguerre-type operators L. From these, we solve two problems about the Poisson semigroup $e^{-t\\sqrt{L}}$. First, we find the largest space of initial data $f$ so that $e^{-t\\sqrt{L}}f(x)\\to f(x)$ at a.e. $x$. Secondly, we characterize the largest class of weights $w$ which admit 2-weight inequalities of the form $\\|\\sup_{0<t\\leq t_0}|e^{-t\\sqrt{L}}f|\\,\\|_{L^p(v)}\\lesssim \\|f\\|_{L^p(w)}$, for some other weight $v$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03966","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"}