{"paper":{"title":"The pointwise convergence of Fourier Series (I). On a conjecture of Konyagin","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Victor Lie","submitted_at":"2014-08-20T19:49:55Z","abstract_excerpt":"We provide a near-complete classification of the Lorentz spaces $\\Lambda_{\\varphi}$ for which the sequence $\\{S_{n}\\}_{n\\in \\mathbb{N}}$ of partial Fourier sums is almost everywhere convergent along lacunary subsequences. Moreover, under mild assumptions on the fundamental function $\\varphi$, we identify $\\Lambda_{\\varphi}:= L\\log\\log L\\log\\log\\log\\log L$ as the \\emph{largest} Lorentz space on which the lacunary Carleson operator is bounded as a map to $L^{1,\\infty}$. In particular, we disprove a conjecture stated by Konyagin in his 2006 ICM address. Our proof relies on a newly introduced conc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4783","kind":"arxiv","version":2},"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"}