{"id":"https://openalex.org/W2076765987","doi":"https://doi.org/10.1142/s0219691315500010","title":"Pseudo-annular decomposition and approximate rate of Calder\u00f3n\u2013Zygmund operators on Heisenberg group","display_name":"Pseudo-annular decomposition and approximate rate of Calder\u00f3n\u2013Zygmund operators on Heisenberg group","publication_year":2014,"publication_date":"2014-12-11","ids":{"openalex":"https://openalex.org/W2076765987","doi":"https://doi.org/10.1142/s0219691315500010","mag":"2076765987"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691315500010","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691315500010","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101964919","display_name":"Pengtao Li","orcid":"https://orcid.org/0000-0003-1202-8468"},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Pengtao Li","raw_affiliation_strings":["College of Mathematics, Qingdao University, Qingdao, Shandong 266071, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics, Qingdao University, Qingdao, Shandong 266071, P. R. China","institution_ids":["https://openalex.org/I108688024"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100457021","display_name":"Heping Liu","orcid":"https://orcid.org/0000-0002-2184-6924"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Heping Liu","raw_affiliation_strings":["LMAM School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China"],"affiliations":[{"raw_affiliation_string":"LMAM School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069295693","display_name":"Lizhong Peng","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lizhong Peng","raw_affiliation_strings":["LMAM School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China"],"affiliations":[{"raw_affiliation_string":"LMAM School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086467460","display_name":"Qixiang Yang","orcid":"https://orcid.org/0000-0003-4966-1910"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qixiang Yang","raw_affiliation_strings":["School of Mathematics and Statics, Wuhan University, Wuhan 430072, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statics, Wuhan University, Wuhan 430072, P. R. China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101964919"],"corresponding_institution_ids":["https://openalex.org/I108688024"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.16792157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"13","issue":"01","first_page":"1550001","last_page":"1550001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998999834060669,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998999834060669,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9991000294685364,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/heisenberg-group","display_name":"Heisenberg group","score":0.7848262786865234},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7280902862548828},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5798907279968262},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4936753213405609},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.484553724527359},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.462448388338089},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43259888887405396},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4296445846557617},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3223201632499695},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18531861901283264},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10015708208084106},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09485381841659546},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.04820889234542847}],"concepts":[{"id":"https://openalex.org/C127519595","wikidata":"https://www.wikidata.org/wiki/Q1601337","display_name":"Heisenberg group","level":2,"score":0.7848262786865234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7280902862548828},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5798907279968262},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4936753213405609},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.484553724527359},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.462448388338089},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43259888887405396},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4296445846557617},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3223201632499695},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18531861901283264},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10015708208084106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09485381841659546},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.04820889234542847},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691315500010","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691315500010","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W48204474","https://openalex.org/W103409674","https://openalex.org/W1584610719","https://openalex.org/W1965252979","https://openalex.org/W1977382531","https://openalex.org/W2018085528","https://openalex.org/W2033639757","https://openalex.org/W2053084186","https://openalex.org/W2085453114","https://openalex.org/W2097818643","https://openalex.org/W2170314752","https://openalex.org/W2593387739","https://openalex.org/W2609921877","https://openalex.org/W6600501402"],"related_works":["https://openalex.org/W2093123991","https://openalex.org/W2122579609","https://openalex.org/W1964016061","https://openalex.org/W2007735529","https://openalex.org/W1560139384","https://openalex.org/W4249580765","https://openalex.org/W2096753949","https://openalex.org/W2357111437","https://openalex.org/W4220985904","https://openalex.org/W2063684714"],"abstract_inverted_index":{"Let":[0],"T":[1,36,46],"be":[2],"a":[3,19],"Calder\u00f3n\u2013Zygmund":[4],"operator":[5],"on":[6],"Heisenberg":[7],"group":[8],"\u210d":[9],"d":[10,51,57],".":[11],"In":[12],"this":[13],"paper,":[14],"by":[15],"wavelets,":[16],"we":[17,39],"introduce":[18],"class":[20],"of":[21,35,45],"pseudo-annular":[22],"operators":[23],"{T":[24],"R":[25,37],"}":[26],"R\u22651":[27],"to":[28,53],"decompose":[29],"T.":[30],"By":[31],"controlling":[32],"the":[33,42],"bandwidth":[34],",":[38],"could":[40],"obtain":[41],"approximate":[43],"rate":[44],"from":[47],"L":[48,54],"2":[49,55],"(\u210d":[50,56],")":[52,58],"at":[59],"an":[60],"ideal":[61],"rate.":[62]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
