{"paper":{"title":"$L^2\\times L^2 \\to L^1$ boundedness criteria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Danqing He, Lenka Slav\\'ikov\\'a, Loukas Grafakos","submitted_at":"2018-02-26T15:28:19Z","abstract_excerpt":"We obtain a sharp $L^2\\times L^2 \\to L^1$ boundedness criterion for a class of bilinear operators associated with a multiplier given by a signed sum of dyadic dilations of a given function, in terms of the $L^q$ integrability of this function; precisely we show that boundedness holds if and only if $q<4$. We discuss applications of this result concerning bilinear rough singular integrals and bilinear dyadic spherical maximal functions.\n  Our second result is an optimal $L^2\\times L^2\\to L^1$ boundedness criterion for bilinear operators associated with multipliers with $L^\\infty$ derivatives. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09400","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"}