{"paper":{"title":"Weighted bounds for variational Walsh-Fourier series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Michael T. Lacey, Yen Do","submitted_at":"2011-12-08T01:16:37Z","abstract_excerpt":"For 1<p<infty, and weight w in A_p, and function f in L^p(w), we show that the r-variation of the\n  Walsh-Fourier sums are finite, for r sufficiently large as function of w. (That r is a function of w is necessary.) This strengthens a result of Hunt-Young and is a weighted extension of a variation norm Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses phase plane analysis and a weighted extension of a variational inequality of Lepingle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1744","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"}