{"paper":{"title":"A sharp estimate of weighted dyadic shifts of complexity 0 and 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Alexander Reznikov, Alexander Volberg, Sergei Treil","submitted_at":"2011-04-28T10:32:03Z","abstract_excerpt":"A simple shortcut to proving sharp weighted estimates for the Martingale Transform and for the dyadic shift of order 1 (and so for the Hilbert transform) is presented. It is a unified proof for these both transforms.\n  Key words: Calder\\on--Zygmund operators, $A_2$ weights, $A_1$ weights, Carleson embedding theorem, Bellman function, dyadic shifts, nonhomogeneous Harmonic Analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5347","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"}