{"id":"https://openalex.org/W4403870584","doi":"https://doi.org/10.3390/axioms13110742","title":"Necessary and Sufficient Conditions for the Boundedness of Multiple Integral Operators with Super-Homogeneous Kernels in Weighted Lebesgue Space","display_name":"Necessary and Sufficient Conditions for the Boundedness of Multiple Integral Operators with Super-Homogeneous Kernels in Weighted Lebesgue Space","publication_year":2024,"publication_date":"2024-10-29","ids":{"openalex":"https://openalex.org/W4403870584","doi":"https://doi.org/10.3390/axioms13110742"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13110742","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13110742","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms13110742","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100359417","display_name":"Hong Yong","orcid":"https://orcid.org/0000-0002-1932-4983"},"institutions":[{"id":"https://openalex.org/I4210113138","display_name":"Guangzhou Automobile Group (China)","ror":"https://ror.org/026fzn952","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210113138"]},{"id":"https://openalex.org/I4400573295","display_name":"Guangzhou Huashang College","ror":"https://ror.org/0546x0d08","country_code":null,"type":"education","lineage":["https://openalex.org/I4400573295"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Hong","raw_affiliation_strings":["Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China","institution_ids":["https://openalex.org/I4210113138","https://openalex.org/I4400573295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102822115","display_name":"Bing He","orcid":null},"institutions":[{"id":"https://openalex.org/I201459984","display_name":"Guangdong University Of Finances and Economics","ror":"https://ror.org/0459pv085","country_code":"CN","type":"education","lineage":["https://openalex.org/I201459984"]},{"id":"https://openalex.org/I32246829","display_name":"Guangdong University of Education","ror":"https://ror.org/0574der91","country_code":"CN","type":"education","lineage":["https://openalex.org/I32246829"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bing He","raw_affiliation_strings":["Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China","institution_ids":["https://openalex.org/I201459984","https://openalex.org/I32246829"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047748352","display_name":"Lijuan Zhang","orcid":"https://orcid.org/0009-0009-8003-1002"},"institutions":[{"id":"https://openalex.org/I4210113138","display_name":"Guangzhou Automobile Group (China)","ror":"https://ror.org/026fzn952","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210113138"]},{"id":"https://openalex.org/I4400573295","display_name":"Guangzhou Huashang College","ror":"https://ror.org/0546x0d08","country_code":null,"type":"education","lineage":["https://openalex.org/I4400573295"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lijuan Zhang","raw_affiliation_strings":["Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China","institution_ids":["https://openalex.org/I4210113138","https://openalex.org/I4400573295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102822115"],"corresponding_institution_ids":["https://openalex.org/I201459984","https://openalex.org/I32246829"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30386179,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"11","first_page":"742","last_page":"742"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","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/T12589","display_name":"Differential Equations and Boundary Problems","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/T11205","display_name":"Numerical methods in inverse problems","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/homogeneous","display_name":"Homogeneous","score":0.7695283889770508},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7520867586135864},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.7058323621749878},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5587128400802612},{"id":"https://openalex.org/keywords/lp-space","display_name":"Lp space","score":0.5549128651618958},{"id":"https://openalex.org/keywords/standard-probability-space","display_name":"Standard probability space","score":0.509039580821991},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5022110939025879},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44758549332618713},{"id":"https://openalex.org/keywords/singular-integral-operators","display_name":"Singular integral operators","score":0.446873277425766},{"id":"https://openalex.org/keywords/lebesgue\u2013stieltjes-integration","display_name":"Lebesgue\u2013Stieltjes integration","score":0.43041619658470154},{"id":"https://openalex.org/keywords/daniell-integral","display_name":"Daniell integral","score":0.37137171626091003},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.24059158563613892},{"id":"https://openalex.org/keywords/fourier-integral-operator","display_name":"Fourier integral operator","score":0.2233792543411255},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.15634024143218994},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10107263922691345},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08156216144561768}],"concepts":[{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.7695283889770508},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7520867586135864},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.7058323621749878},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5587128400802612},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.5549128651618958},{"id":"https://openalex.org/C12871628","wikidata":"https://www.wikidata.org/wiki/Q7598372","display_name":"Standard probability space","level":2,"score":0.509039580821991},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5022110939025879},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44758549332618713},{"id":"https://openalex.org/C2992640183","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral operators","level":4,"score":0.446873277425766},{"id":"https://openalex.org/C43323394","wikidata":"https://www.wikidata.org/wiki/Q3799278","display_name":"Lebesgue\u2013Stieltjes integration","level":5,"score":0.43041619658470154},{"id":"https://openalex.org/C134810832","wikidata":"https://www.wikidata.org/wiki/Q2996956","display_name":"Daniell integral","level":4,"score":0.37137171626091003},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.24059158563613892},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.2233792543411255},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.15634024143218994},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10107263922691345},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08156216144561768},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13110742","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13110742","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:63317954fe5440599be8fdf24a89fcfa","is_oa":false,"landing_page_url":"https://doaj.org/article/63317954fe5440599be8fdf24a89fcfa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 11, p 742 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13110742","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13110742","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1651788694","https://openalex.org/W1994518041","https://openalex.org/W2017761485","https://openalex.org/W2031752698","https://openalex.org/W2070911304","https://openalex.org/W2090922263","https://openalex.org/W2181806288","https://openalex.org/W2314471702","https://openalex.org/W2333527412","https://openalex.org/W2782779200","https://openalex.org/W3012352405","https://openalex.org/W4383878394","https://openalex.org/W4386600784","https://openalex.org/W4387850954","https://openalex.org/W6636749042","https://openalex.org/W6685825500","https://openalex.org/W6857520039"],"related_works":["https://openalex.org/W2810450715","https://openalex.org/W2171127053","https://openalex.org/W4386510778","https://openalex.org/W2778407230","https://openalex.org/W2592407816","https://openalex.org/W1974574863","https://openalex.org/W2090550831","https://openalex.org/W1528126182","https://openalex.org/W2164391627","https://openalex.org/W1560766029"],"abstract_inverted_index":{"Super-homogeneous":[0],"functions":[1,10],"including":[2],"homogeneous":[3],"functions,":[4,6],"quasi-homogeneous":[5],"and":[7,54,57,63],"several":[8],"non-homogeneous":[9],"are":[11,29,68],"considered.":[12],"Using":[13],"the":[14,18,34,37,55,64],"weight":[15],"function":[16],"method,":[17],"construction":[19,38],"conditions":[20,59],"of":[21,40],"Hilbert-type":[22],"multiple":[23,42],"integral":[24,43],"inequalities":[25],"with":[26,45],"super-homogeneous":[27,46],"kernels":[28,47],"first":[30],"discussed.":[31],"Then,":[32],"using":[33],"obtained":[35],"results,":[36],"problem":[39],"bounded":[41],"operators":[44],"in":[48],"weighted":[49],"Lebesgue":[50],"space":[51],"is":[52],"discussed,":[53],"necessary":[56],"sufficient":[58],"for":[60],"operator":[61,65],"boundedness":[62],"norm":[66],"formula":[67],"obtained.":[69]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
