{"paper":{"title":"Two-weight $L^p$-$L^q$ bounds for positive dyadic operators: unified approach to $p\\leq q$ and $p>q$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kangwei Li, Timo S. H\\\"anninen, Tuomas P. Hyt\\\"onen","submitted_at":"2014-12-08T14:52:11Z","abstract_excerpt":"We characterize the $L^p(\\sigma)\\to L^q(\\omega)$ boundedness of positive dyadic operators of the form $\n  T(f\\sigma)=\\sum_{Q\\in\\mathscr{D}}\\lambda_Q\\int_Q f\\,\\mathrm{d}\\sigma\\cdot 1_Q, $ and the $L^{p_1}(\\sigma_1)\\times L^{p_2}(\\sigma_2)\\to L^q(\\omega)$ boundedness of their bilinear analogues, for arbitrary locally finite measures $\\sigma,\\sigma_1,\\sigma_2,\\omega$. In the linear case, we unify the existing \"Sawyer testing\" (for $p\\leq q$) and \"Wolff potential\" (for $p>q$) characterizations into a new \"sequential testing\" characterization valid in all cases. We extend these ideas to the bilinea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2593","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"}