{"paper":{"title":"Products of Functions in ${\\mathop\\mathrm{BMO}}({\\mathcal X})$ and $H^1_{\\rm at}({\\mathcal X})$ via Wavelets over Spaces of Homogeneous Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Xing Fu, Yiyu Liang","submitted_at":"2015-06-19T08:35:31Z","abstract_excerpt":"Let $({\\mathcal X},d,\\mu)$ be a metric measure space of homogeneous type in the sense of R. R. Coifman and G. Weiss and $H^1_{\\rm at}({\\mathcal X})$ be the atomic Hardy space. Via orthonormal bases of regular wavelets and spline functions recently constructed by P. Auscher and T. Hyt\\\"onen, the authors prove that the product $f\\times g$ of $f\\in H^1_{\\rm at}({\\mathcal X})$ and $g\\in\\mathop\\mathrm{BMO}({\\mathcal X})$, viewed as a distribution, can be written into a sum of two bounded bilinear operators, respectively, from $H^1_{\\rm at}({\\mathcal X})\\times\\mathop\\mathrm{BMO}({\\mathcal X})$ into "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05910","kind":"arxiv","version":3},"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"}