{"id":"https://openalex.org/W2144543987","doi":"https://doi.org/10.37236/330","title":"Some Inequalities in Functional Analysis, Combinatorics, and Probability Theory","display_name":"Some Inequalities in Functional Analysis, Combinatorics, and Probability Theory","publication_year":2010,"publication_date":"2010-04-05","ids":{"openalex":"https://openalex.org/W2144543987","doi":"https://doi.org/10.37236/330","mag":"2144543987"},"language":"en","primary_location":{"id":"doi:10.37236/330","is_oa":true,"landing_page_url":"https://doi.org/10.37236/330","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r58/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r58/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087224675","display_name":"Chunrong Feng","orcid":"https://orcid.org/0000-0001-5244-4664"},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]},{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Chunrong Feng","raw_affiliation_strings":["Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China & Department of Mathematical Sciences,","Loughborough University, Leics, LE11 3TU, UK","Shanghai Jiao Tong Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China & Department of Mathematical Sciences,","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Loughborough University, Leics, LE11 3TU, UK","institution_ids":["https://openalex.org/I143804889"]},{"raw_affiliation_string":"Shanghai Jiao Tong Univ","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000853716","display_name":"Liangpan Li","orcid":"https://orcid.org/0000-0001-8655-348X"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Liangpan Li","raw_affiliation_strings":["Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100766006","display_name":"Jian Shen","orcid":"https://orcid.org/0000-0001-8101-9528"},"institutions":[{"id":"https://openalex.org/I13511017","display_name":"Texas State University","ror":"https://ror.org/05h9q1g27","country_code":"US","type":"education","lineage":["https://openalex.org/I13511017"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jian Shen","raw_affiliation_strings":["Department of Mathematics, Texas State University, San Marcos, TX 78666, USA","Texas\u00a0State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas State University, San Marcos, TX 78666, USA","institution_ids":["https://openalex.org/I13511017"]},{"raw_affiliation_string":"Texas\u00a0State University","institution_ids":["https://openalex.org/I13511017"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000853716"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":1.9294,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.85150726,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"17","issue":"1","first_page":null,"last_page":null},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/mathematics","display_name":"Mathematics","score":0.8922786712646484},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.6269580721855164},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6213883757591248},{"id":"https://openalex.org/keywords/extremal-combinatorics","display_name":"Extremal combinatorics","score":0.5782114267349243},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.560127854347229},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.47825896739959717},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4566276967525482},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35191813111305237},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2642700970172882},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05767503380775452}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8922786712646484},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6269580721855164},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6213883757591248},{"id":"https://openalex.org/C549619432","wikidata":"https://www.wikidata.org/wiki/Q5422299","display_name":"Extremal combinatorics","level":2,"score":0.5782114267349243},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.560127854347229},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.47825896739959717},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4566276967525482},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35191813111305237},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2642700970172882},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05767503380775452},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/330","is_oa":true,"landing_page_url":"https://doi.org/10.37236/330","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r58/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:durham-repository.worktribe.com:1282324","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1282324","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.37236/330","is_oa":true,"landing_page_url":"https://doi.org/10.37236/330","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r58/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4000000059604645}],"awards":[{"id":"https://openalex.org/G3110580028","display_name":"SGER:  A Novel Information Model for Efficient Routing Protocols in Delay Tolerant Networks with General Mobility","funder_award_id":"0835834","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3144391295","display_name":null,"funder_award_id":"(ARP 003615-0039-2007)","funder_id":"https://openalex.org/F4320308138","funder_display_name":"Texas Higher Education Coordinating Board"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308138","display_name":"Texas Higher Education Coordinating Board","ror":"https://ror.org/05as1qb59"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2144543987.pdf","grobid_xml":"https://content.openalex.org/works/W2144543987.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1229215291","https://openalex.org/W1610447576","https://openalex.org/W1969061779","https://openalex.org/W1982919008","https://openalex.org/W1997424790","https://openalex.org/W2005225596","https://openalex.org/W2021851424","https://openalex.org/W2045794269","https://openalex.org/W2083468009","https://openalex.org/W2092271237","https://openalex.org/W2103735764","https://openalex.org/W2316919907","https://openalex.org/W2791520396","https://openalex.org/W2963096774","https://openalex.org/W2969734899","https://openalex.org/W3100507412","https://openalex.org/W4229996378","https://openalex.org/W4232507844","https://openalex.org/W4245362612"],"related_works":["https://openalex.org/W2935028240","https://openalex.org/W2047131671","https://openalex.org/W3007838749","https://openalex.org/W2181432034","https://openalex.org/W4237951173","https://openalex.org/W2905264121","https://openalex.org/W4214479031","https://openalex.org/W4385826423","https://openalex.org/W3004234532","https://openalex.org/W4238658364"],"abstract_inverted_index":{"The":[0],"main":[1],"purpose":[2],"of":[3,22,34],"this":[4],"paper":[5],"is":[6],"to":[7],"show":[8],"that":[9],"many":[10],"inequalities":[11],"in":[12,27],"functional":[13],"analysis,":[14],"probability":[15],"theory":[16],"and":[17,43],"combinatorics":[18],"are":[19,46],"immediate":[20],"corollaries":[21],"the":[23,35,39],"best":[24],"approximation":[25],"theorem":[26],"inner":[28],"product":[29],"spaces.":[30],"Besides,":[31],"as":[32],"applications":[33],"de":[36],"Caen-Selberg":[37],"inequality,":[38],"finite":[40],"field":[41],"Kakeya":[42],"Nikodym":[44],"problems":[45],"also":[47],"studied.":[48]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}