{"id":"https://openalex.org/W7223007553","doi":"https://doi.org/10.48550/arxiv.2610.26415","title":"Triebel - Lizorkin spaces of dominating mixed smoothness are algebras with respect to pointwise multiplication","display_name":"Triebel - Lizorkin spaces of dominating mixed smoothness are algebras with respect to pointwise multiplication","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7223007553","doi":"https://doi.org/10.48550/arxiv.2610.26415"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.26415","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26415","pdf_url":"https://arxiv.org/pdf/2610.26415","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.26415","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100574316","display_name":"Van Kien Nguyen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210093659","display_name":"University of Transport and Communications","ror":"https://ror.org/006qk6d61","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210093659"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Nguyen, Van Kien","raw_affiliation_strings":["University of Transport and Communications No 3 Cau Giay Street , Lang Ward , Hanoi , Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Transport and Communications No 3 Cau Giay Street , Lang Ward , Hanoi , Vietnam","institution_ids":["https://openalex.org/I4210093659"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100574316"],"corresponding_institution_ids":["https://openalex.org/I4210093659"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.8490999937057495,"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":0.8490999937057495,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.08110000193119049,"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"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.02449999935925007,"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/triebel-lizorkin-spaces","display_name":"Triebel-Lizorkin spaces","score":0.9829999804496765},{"id":"https://openalex.org/keywords/dominating-mixed-smoothness","display_name":"dominating mixed smoothness","score":0.9819999933242798},{"id":"https://openalex.org/keywords/pointwise-multipliers","display_name":"pointwise multipliers","score":0.8270000219345093},{"id":"https://openalex.org/keywords/algebra","display_name":"algebra","score":0.6899999976158142},{"id":"https://openalex.org/keywords/pointwise-multiplication","display_name":"pointwise multiplication","score":0.9710000157356262},{"id":"https://openalex.org/keywords/function-spaces","display_name":"function spaces","score":0.9160000085830688}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.9052000045776367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.814300000667572},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.7192000150680542},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.506600022315979},{"id":"https://openalex.org/C27156116","wikidata":"https://www.wikidata.org/wiki/Q1778098","display_name":"Pointwise convergence","level":3,"score":0.44830000400543213},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.3946000039577484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3345000147819519},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.26170000433921814},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.24480000138282776}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.26415","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26415","pdf_url":"https://arxiv.org/pdf/2610.26415","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.26415","doi":"https://doi.org/10.48550/arxiv.2610.26415","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.26415","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.26415","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26415","pdf_url":"https://arxiv.org/pdf/2610.26415","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G8385092862","display_name":"Data Driven High-Dimensional Approximation - Mathematical Analysis and Computing","funder_award_id":"229568","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223007553.pdf","grobid_xml":"https://content.openalex.org/works/W7223007553.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2512591573","https://openalex.org/W1972615078","https://openalex.org/W2611275698","https://openalex.org/W2801825434","https://openalex.org/W2773969677","https://openalex.org/W2885724988","https://openalex.org/W2529580485","https://openalex.org/W7123352984","https://openalex.org/W72921533","https://openalex.org/W2024698358"],"abstract_inverted_index":{"We":[0],"continue":[1],"our":[2],"investigations":[3],"on":[4],"pointwise":[5,36],"multipliers":[6],"for":[7],"spaces":[8,26],"of":[9,27],"dominating":[10,28],"mixed":[11,29],"smoothness.":[12],"In":[13],"this":[14],"paper":[15],"we":[16],"prove":[17],"that":[18],"under":[19],"a":[20],"certain":[21],"conditions":[22],"Triebel":[23],"-":[24],"Lizorkin":[25],"smoothness":[30],"form":[31],"algebras":[32],"with":[33],"respect":[34],"to":[35],"multiplication.":[37]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-21T00:00:00"}
