{"id":"https://openalex.org/W2164222693","doi":"https://doi.org/10.1090/s0002-9947-2013-05965-x","title":"Centered Hardy-Littlewood maximal functions on Heisenberg type groups","display_name":"Centered Hardy-Littlewood maximal functions on Heisenberg type groups","publication_year":2013,"publication_date":"2013-09-26","ids":{"openalex":"https://openalex.org/W2164222693","doi":"https://doi.org/10.1090/s0002-9947-2013-05965-x","mag":"2164222693"},"language":"en","primary_location":{"id":"doi:10.1090/s0002-9947-2013-05965-x","doi":"https://doi.org/10.1090/s0002-9947-2013-05965-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-2013-05965-x","pdf_url":"https://www.ams.org/tran/2014-366-03/S0002-9947-2013-05965-X/S0002-9947-2013-05965-X.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2164222693"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/tran/2014-366-03/S0002-9947-2013-05965-X/S0002-9947-2013-05965-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100664112","display_name":"Hong-Quan Li","orcid":"https://orcid.org/0000-0003-3822-6999","observed_orcids":["https://orcid.org/0000-0003-3822-6999"]},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hong-Quan Li","raw_affiliation_strings":["School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai 200433, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai 200433, People\u2019s Republic of China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101845561","display_name":"Bin Qian","orcid":"https://orcid.org/0000-0001-5110-2494","observed_orcids":["https://orcid.org/0000-0001-5110-2494"]},"institutions":[{"id":"https://openalex.org/I21741975","display_name":"Suzhou University of Technology","ror":"https://ror.org/05g6ben79","country_code":"CN","type":"education","lineage":["https://openalex.org/I21741975"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bin Qian","raw_affiliation_strings":["School of Mathematics and Statistics, Changshu Institute of Technology 215500, Changshu, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Changshu Institute of Technology 215500, Changshu, People\u2019s Republic of China","institution_ids":["https://openalex.org/I21741975"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9776,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.67703338,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"366","issue":"3","first_page":"1497","last_page":"1524"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9984999895095825,"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":0.9984999895095825,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.00039999998989515007,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0003000000142492354,"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/heisenberg-type-groups","display_name":"Heisenberg type groups","score":0.9940000176429749},{"id":"https://openalex.org/keywords/carnot-caratheodory-distance","display_name":"Carnot-Carath\u00e9odory distance","score":0.9919999837875366},{"id":"https://openalex.org/keywords/poisson-kernel","display_name":"Poisson kernel","score":0.7590000033378601},{"id":"https://openalex.org/keywords/fractional-laplacian","display_name":"fractional Laplacian","score":0.8659999966621399},{"id":"https://openalex.org/keywords/bessel-functions","display_name":"Bessel functions","score":0.9350000023841858},{"id":"https://openalex.org/keywords/legendre-functions","display_name":"Legendre functions","score":0.996999979019165},{"id":"https://openalex.org/keywords/weak-type-1-1-estimates","display_name":"weak type (1,1) estimates","score":0.7360000014305115},{"id":"https://openalex.org/keywords/l1-norm","display_name":"L1 norm","score":0.3199999928474426}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8942017555236816},{"id":"https://openalex.org/C127519595","wikidata":"https://www.wikidata.org/wiki/Q1601337","display_name":"Heisenberg group","level":2,"score":0.694455623626709},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6663816571235657},{"id":"https://openalex.org/C188422159","wikidata":"https://www.wikidata.org/wiki/Q6795639","display_name":"Maximal function","level":2,"score":0.571864902973175},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5699213743209839},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.5139098167419434},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4311954081058502},{"id":"https://openalex.org/C8077415","wikidata":"https://www.wikidata.org/wiki/Q2596534","display_name":"Poisson kernel","level":2,"score":0.41824156045913696},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34325915575027466},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0002-9947-2013-05965-x","doi":"https://doi.org/10.1090/s0002-9947-2013-05965-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-2013-05965-x","pdf_url":"https://www.ams.org/tran/2014-366-03/S0002-9947-2013-05965-X/S0002-9947-2013-05965-X.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0002-9947-2013-05965-x","doi":"https://doi.org/10.1090/s0002-9947-2013-05965-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-2013-05965-x","pdf_url":"https://www.ams.org/tran/2014-366-03/S0002-9947-2013-05965-X/S0002-9947-2013-05965-X.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1193298573","display_name":null,"funder_award_id":"NCET-09","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6008654799","display_name":null,"funder_award_id":"11201040","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322829","display_name":"Universit\u00e9 de Toulouse","ror":"https://ror.org/01ahyrz84"},{"id":"https://openalex.org/F4320334924","display_name":"Program for New Century Excellent Talents in University","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320336023","display_name":"Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2164222693.pdf","grobid_xml":"https://content.openalex.org/works/W2164222693.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W294638877","https://openalex.org/W1556192255","https://openalex.org/W1599382417","https://openalex.org/W1964016061","https://openalex.org/W1966305649","https://openalex.org/W1973517775","https://openalex.org/W1983476312","https://openalex.org/W1988967439","https://openalex.org/W1995654105","https://openalex.org/W2000960107","https://openalex.org/W2006195050","https://openalex.org/W2019789100","https://openalex.org/W2039994238","https://openalex.org/W2053061709","https://openalex.org/W2054690979","https://openalex.org/W2081338783","https://openalex.org/W2099451168","https://openalex.org/W2158299616","https://openalex.org/W2331309905","https://openalex.org/W2596323328","https://openalex.org/W2963819382","https://openalex.org/W3107383929","https://openalex.org/W3113221786","https://openalex.org/W4230941884","https://openalex.org/W6612146252","https://openalex.org/W6676006349"],"related_works":["https://openalex.org/W4403466095","https://openalex.org/W2039994238","https://openalex.org/W1991315983","https://openalex.org/W7154694983","https://openalex.org/W2522154085","https://openalex.org/W4416416616","https://openalex.org/W2949111285","https://openalex.org/W1978462868","https://openalex.org/W7161122255","https://openalex.org/W2906953866"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"by":[3,80,92],"establishing":[4],"uniform":[5],"lower":[6],"bounds":[7],"for":[8,49,102],"the":[9,17,30,74,81,85,93],"Poisson":[10],"kernel":[11],"and":[12,36,54],"$(-\\Delta":[13],")^{-\\frac":[14],"12}$":[15],"on":[16],"Heisenberg":[18],"type":[19],"group":[20],"$\\mathbb":[21],"{H}(2n,m)$":[22],"with":[23],"$m":[24],"\\geq":[25],"2$,":[26],"which":[27],"follow":[28],"from":[29],"various":[31],"properties":[32],"of":[33,107],"Bessel":[34],"functions":[35],"Legendre":[37],"functions,":[38],"we":[39,66,96],"prove":[40,97],"that":[41],"there":[42],"exists":[43],"a":[44],"constant":[45,104],"$A>0$":[46],"such":[47],"that,":[48],"all":[50,55],"$f\\in":[51],"L^1(\\mathbb":[52],"{H}(2n,m))$":[53],"$n,m":[56],"\\in":[57],"\\mathbb":[58],"{N}^*$":[59],"satisfying":[60],"$4":[61],"\\leq":[62],"m^2\\ll":[63],"\\log":[64],"n$,":[65],"have":[67],"$\\|M_{K}f\\|_{L^{1,\\infty":[68],"}}\\le":[69,99],"An\\|f\\|_1$,":[70],"where":[71],"$M_{K}$":[72],"denotes":[73],"centered":[75,86],"Hardy-Littlewood":[76,87],"maximal":[77,88],"function":[78,89],"defined":[79,91],"Kor\u00e1nyi":[82],"norm.":[83],"For":[84],"$M_{CC}$":[90],"Carnot-Carath\u00e9dory":[94],"distance,":[95],"$\\|M_{CC}f\\|_{L^{1,\\infty":[98],"A(m)n\\|f\\|_1$":[100],"holds":[101],"some":[103],"$A(m)$":[105],"independent":[106],"$n$.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2016-06-24T00:00:00"}