{"paper":{"title":"Bilinear decompositions for the product space $H^1_L\\times BMO_L$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Luong Dang Ky","submitted_at":"2012-04-13T16:28:13Z","abstract_excerpt":"In this paper, we improve a recent result by Li and Peng on products of functions in $H_L^1(\\bR^d)$ and $BMO_L(\\bR^d)$, where $L=-\\Delta+V$ is a Schr\\\"odinger operator with $V$ satisfying an appropriate reverse H\\\"older inequality. More precisely, we prove that such products may be written as the sum of two continuous bilinear operators, one from $H_L^1(\\bR^d)\\times BMO_L(\\bR^d) $ into $L^1(\\bR^d)$, the other one from $H^1_L(\\bR^d)\\times BMO_L(\\bR^d) $ into $H^{\\log}(\\bR^d)$, where the space $H^{\\log}(\\bR^d)$ is the set of distributions $f$ whose grand maximal function $\\mathfrak Mf$ satisfies"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3041","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"}