{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:P3AQVG4ISRWRKKTW4ADSLVAP6S","short_pith_number":"pith:P3AQVG4I","schema_version":"1.0","canonical_sha256":"7ec10a9b88946d152a76e00725d40ff4b73ce5cdfb382c72fc7251b76f90ab6b","source":{"kind":"arxiv","id":"1607.02617","version":3},"attestation_state":"computed","paper":{"title":"The H\\\"ormander Multiplier Theorem III: The complete bilinear case via interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Hanh Van Nguyen, Loukas Grafakos","submitted_at":"2016-07-09T14:41:31Z","abstract_excerpt":"We develop a special multilinear complex interpolation theorem that allows us to prove an optimal version of the bilinear H\\\"ormander multiplier theorem concerning symbols that lie in the Sobolev space $L^r_s(\\mathbb R^{2n})$, $2\\le r<\\infty$, $rs>2n$, uniformly over all annuli. More precisely, given a smoothness index $s$, we find the largest open set of indices $(1/p_1,1/p_2 )$ for which we have boundedness for the associated bilinear multiplier operator from $L^{p_1}(\\mathbb R^{ n})\\times L^{p_2} (\\mathbb R^{ n})$ to $ L^p(\\mathbb R^{ n})$ when $1/p=1/p_1+1/p_2$, $12n$, uniformly over all annuli. More precisely, given a smoothness index $s$, we find the largest open set of indices $(1/p_1,1/p_2 )$ for which we have boundedness for the associated bilinear multiplier operator from $L^{p_1}(\\mathbb R^{ n})\\times L^{p_2} (\\mathbb R^{ n})$ to $ L^p(\\mathbb R^{ n})$ when $1/p=1/p_1+1/p_2$, $1