{"paper":{"title":"Weighted estimates for dyadic paraproducts and t-Haar multipiers with complexity (m,n)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jean Carlo Moraes, Mar\\'ia Cristina Pereyra","submitted_at":"2011-08-15T22:33:03Z","abstract_excerpt":"We extend the definitions of dyadic paraproduct and t-Haar multipliers to dyadic operators that depend on the complexity (m,n), for m and n positive integers. We will use the ideas developed by Nazarov and Volberg to prove that the weighted L^2(w)-norm of a paraproduct with complexity (m,n) associated to a function b\\in BMO, depends linearly on the A_2-characteristic of the weight w, linearly on the BMO-norm of b, and polynomially in the complexity. This argument provides a new proof of the linear bound for the dyadic paraproduct (the one with complexity (0,0)). Also we prove that the L^2-norm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3109","kind":"arxiv","version":4},"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"}