{"id":"https://openalex.org/W2168538265","doi":"https://doi.org/10.1112/jlms/jdu044","title":"Vector-valued inequalities for families of bilinear Hilbert transforms and applications to bi-parameter problems","display_name":"Vector-valued inequalities for families of bilinear Hilbert transforms and applications to bi-parameter problems","publication_year":2014,"publication_date":"2014-09-04","ids":{"openalex":"https://openalex.org/W2168538265","doi":"https://doi.org/10.1112/jlms/jdu044","mag":"2168538265"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdu044","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu044","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1203.3251","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026470282","display_name":"Prabath Silva","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Prabath Silva","raw_affiliation_strings":["Department of Mathematics, Indiana University, 831 East 3rd Street, Bloomington, IN 47405, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indiana University, 831 East 3rd Street, Bloomington, IN 47405, USA","institution_ids":["https://openalex.org/I4210119109"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026470282"],"corresponding_institution_ids":["https://openalex.org/I4210119109"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":4.5826,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.94636183,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"90","issue":"3","first_page":"695","last_page":"724"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.8825778961181641},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7341076135635376},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.7300106287002563},{"id":"https://openalex.org/keywords/hilbert-transform","display_name":"Hilbert transform","score":0.559657633304596},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5540640354156494},{"id":"https://openalex.org/keywords/bilinear-map","display_name":"Bilinear map","score":0.552116870880127},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5133504271507263},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.49289608001708984},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.47282588481903076},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4711771607398987},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.46409955620765686},{"id":"https://openalex.org/keywords/bilinear-transform","display_name":"Bilinear transform","score":0.46191003918647766},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4456784427165985},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33932140469551086},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3256009817123413},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11428561806678772},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.08286288380622864},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06680676341056824}],"concepts":[{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.8825778961181641},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7341076135635376},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.7300106287002563},{"id":"https://openalex.org/C28799612","wikidata":"https://www.wikidata.org/wiki/Q685437","display_name":"Hilbert transform","level":3,"score":0.559657633304596},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5540640354156494},{"id":"https://openalex.org/C142685569","wikidata":"https://www.wikidata.org/wiki/Q1086961","display_name":"Bilinear map","level":3,"score":0.552116870880127},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5133504271507263},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.49289608001708984},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.47282588481903076},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4711771607398987},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.46409955620765686},{"id":"https://openalex.org/C109786386","wikidata":"https://www.wikidata.org/wiki/Q861804","display_name":"Bilinear transform","level":4,"score":0.46191003918647766},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4456784427165985},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33932140469551086},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3256009817123413},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11428561806678772},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.08286288380622864},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06680676341056824},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C36390408","wikidata":"https://www.wikidata.org/wiki/Q1163067","display_name":"Digital filter","level":3,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1112/jlms/jdu044","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu044","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1203.3251","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1203.3251","pdf_url":"https://arxiv.org/pdf/1203.3251","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.756.1313","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.756.1313","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1203.3251.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1203.3251","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1203.3251","pdf_url":"https://arxiv.org/pdf/1203.3251","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.5799999833106995,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W592834996","https://openalex.org/W1579825913","https://openalex.org/W1970408056","https://openalex.org/W1989946594","https://openalex.org/W1993031273","https://openalex.org/W2007927352","https://openalex.org/W2008541304","https://openalex.org/W2010183658","https://openalex.org/W2081601543","https://openalex.org/W2089324911","https://openalex.org/W2593473467","https://openalex.org/W2951147838","https://openalex.org/W3101087383"],"related_works":["https://openalex.org/W3111804415","https://openalex.org/W1969781932","https://openalex.org/W4388647805","https://openalex.org/W3183197589","https://openalex.org/W2789866466","https://openalex.org/W2055191795","https://openalex.org/W113171773","https://openalex.org/W1963546854","https://openalex.org/W3129644063","https://openalex.org/W2080806178"],"abstract_inverted_index":{"Muscalu,":[0],"Pipher,":[1],"Tao":[2],"and":[3],"Thiele":[4],"showed":[5,32],"that":[6,33],"the":[7,22,28,34,53,58],"tensor":[8,35],"product":[9,36],"between":[10],"two":[11,38],"one-dimensional":[12],"paraproducts":[13],"(also":[14],"known":[15],"as":[16],"a":[17,50,64,72,90],"bi-parameter":[18],"paraproduct)":[19],"satisfies":[20],"all":[21],"expected":[23],"L":[24,54],"p":[25,55],"bounds.":[26],"In":[27],"same":[29],"paper,":[30],"they":[31],"of":[37,57,75,92],"bilinear":[39,59,80,93],"Hilbert":[40,60,94],"transforms":[41],"is":[42],"unbounded":[43],"in":[44],"any":[45],"range.":[46],"They":[47],"also":[48],"raised":[49],"question":[51,69],"concerning":[52],"boundedness":[56],"transform":[61],"tensored":[62],"with":[63],"paraproduct.":[65],"We":[66],"answer":[67],"their":[68],"by":[70],"obtaining":[71],"wide":[73],"range":[74],"estimates":[76,88],"for":[77,89],"this":[78],"hybrid":[79],"operator.":[81],"Our":[82],"method":[83],"relies":[84],"on":[85],"new":[86],"vector-valued":[87],"family":[91],"transforms.":[95]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
