{"paper":{"title":"Paraproducts and Products of functions in $BMO(\\mathbb R^n)$ and $H^1(\\mathbb R^n)$ through wavelets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Aline Bonami (MAPMO), Luong Dang Ky (MAPMO), Sandrine Grellier (MAPMO)","submitted_at":"2011-03-09T16:17:14Z","abstract_excerpt":"In this paper, we prove that the product (in the distribution sense) of two functions, which are respectively in $ \\BMO(\\bR^n)$ and $\\H^1(\\bR^n)$, may be written as the sum of two continuous bilinear operators, one from $\\H^1(\\bR^n)\\times \\BMO(\\bR^n) $ into $L^1(\\bR^n)$, the other one from $\\H^1(\\bR^n)\\times \\BMO(\\bR^n) $ into a new kind of Hardy-Orlicz space denoted by $\\H^{\\log}(\\bR^n)$. More precisely, the space $\\H^{\\log}(\\bR^n)$ is the set of distributions $f$ whose grand maximal function $\\mathcal Mf$ satisfies $$\\int_{\\mathbb R^n} \\frac {|\\mathcal M f(x)|}{\\log(e+|x|) +\\log (e+ |\\mathca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1822","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"}