{"paper":{"title":"Bilinear pseudo-differential operators with exotic symbols, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Akihiko Miyachi, Naohito Tomita","submitted_at":"2018-01-21T00:40:57Z","abstract_excerpt":"The boundedness from $H^p \\times L^2$ to $L^r$, $1/p+1/2=1/r$, and from $H^p \\times L^{\\infty}$ to $L^p$ of bilinear pseudo-differential operators is proved under the assumption that their symbols are in the bilinear H\\\"ormander class $BS^m_{\\rho,\\rho}$, $0 \\le \\rho <1$, of critical order $m$, where $H^p$ is the Hardy space. This combined with the previous results of the same authors establishes the sharp boundedness from $H^p \\times H^q$ to $L^r$, $1/p+1/q=1/r$, of those operators in the full range $0< p, q \\le \\infty$, where $L^r$ is replaced by $BMO$ if $r=\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06745","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"}