{"paper":{"title":"Endpoint estimates for the maximal function over prime numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.NT"],"primary_cat":"math.DS","authors_text":"Bartosz Trojan","submitted_at":"2019-07-10T14:31:20Z","abstract_excerpt":"Given an ergodic dynamical system $(X, \\mathcal{B}, \\mu, T)$, we prove that for each function $f$ belonging to the Orlicz space $L(\\log L)^2(\\log \\log L)(X, \\mu)$, the ergodic averages \\[ \\frac{1}{\\pi(N)} \\sum_{p \\in \\mathbb{P}_N} f\\big(T^p x\\big), \\] converge for $\\mu$-almost all $x \\in X$, where $\\mathbb{P}_N$ is the set of prime numbers not larger that $N$ and $\\pi(N) = \\# \\mathbb{P}_N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04753","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"}