{"paper":{"title":"Endpoint Mapping properties of the Littlewood-Paley square function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Odysseas Bakas","submitted_at":"2016-12-30T19:48:36Z","abstract_excerpt":"In this note we give an alternative proof of a theorem due to Bourgain \\cite{Bourgain} concerning the growth of the constant in the Littlewood-Paley inequality on $\\mathbb{T}$ as $p \\rightarrow 1^+$. Our argument is based on the endpoint mapping properties of Marcinkiewicz multiplier operators, obtained by Tao and Wright in \\cite{TW}, and on Tao's converse extrapolation theorem \\cite{Tao}. Our method also establishes the growth of the constant in the Littlewood-Paley inequality on $\\mathbb{T}^n$ as $p \\rightarrow 1^+$. Furthermore, we obtain sharp weak-type inequalities for the Littlewood-Pale"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09573","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"}