{"id":"https://openalex.org/W7213403722","doi":"https://doi.org/10.48550/arxiv.2609.16902","title":"Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups, II: Pointwise Multiplication, Localization, Differences","display_name":"Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups, II: Pointwise Multiplication, Localization, Differences","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7213403722","doi":"https://doi.org/10.48550/arxiv.2609.16902"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.16902","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16902","pdf_url":"https://arxiv.org/pdf/2609.16902","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/2609.16902","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036200704","display_name":"Mattia Calzi","orcid":"https://orcid.org/0000-0002-5094-9383","observed_orcids":["https://orcid.org/0000-0002-5094-9383"]},"institutions":[{"id":"https://openalex.org/I2802148964","display_name":"Istituto Nazionale di Alta Matematica Francesco Severi","ror":"https://ror.org/01vx64p53","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I2802148964"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Calzi, Mattia","raw_affiliation_strings":["Istituto Nazionale di Alta Matematica (INdAM)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Istituto Nazionale di Alta Matematica (INdAM)","institution_ids":["https://openalex.org/I2802148964"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5036200704"],"corresponding_institution_ids":["https://openalex.org/I2802148964"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":4,"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":0.9761000275611877,"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":0.9761000275611877,"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":0.0203000009059906,"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":0.0005000000237487257,"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/besov-spaces","display_name":"Besov spaces","score":0.9990000128746033},{"id":"https://openalex.org/keywords/triebel-lizorkin-spaces","display_name":"Triebel-Lizorkin spaces","score":1.0},{"id":"https://openalex.org/keywords/pointwise-multipliers","display_name":"pointwise multipliers","score":0.9549999833106995}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8418999910354614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6650000214576721},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5386999845504761},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4909999966621399},{"id":"https://openalex.org/C27156116","wikidata":"https://www.wikidata.org/wiki/Q1778098","display_name":"Pointwise convergence","level":3,"score":0.4153999984264374},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.4077000021934509},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.38600000739097595},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3521000146865845},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C129698243","wikidata":"https://www.wikidata.org/wiki/Q526261","display_name":"Besov space","level":5,"score":0.32249999046325684},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3158999979496002},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29010000824928284},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.27950000762939453}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.16902","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16902","pdf_url":"https://arxiv.org/pdf/2609.16902","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.2609.16902","doi":"https://doi.org/10.48550/arxiv.2609.16902","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.16902","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:2609.16902","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16902","pdf_url":"https://arxiv.org/pdf/2609.16902","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213403722.pdf","grobid_xml":"https://content.openalex.org/works/W7213403722.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W7213372510","https://openalex.org/W7213411014","https://openalex.org/W7213419554"],"related_works":["https://openalex.org/W7214037519","https://openalex.org/W7213419554","https://openalex.org/W7213411014","https://openalex.org/W7213372510","https://openalex.org/W4385652300","https://openalex.org/W2984539704","https://openalex.org/W4408617091","https://openalex.org/W2920904962","https://openalex.org/W2885724988","https://openalex.org/W3123108587"],"abstract_inverted_index":{"We":[0],"continue":[1],"to":[2],"develop":[3],"a":[4,17],"theory":[5],"of":[6],"Besov":[7],"and":[8,31],"Triebel-Lizorkin":[9],"spaces":[10],"associated":[11],"with":[12],"weighted":[13],"subcoercive":[14],"operators":[15],"on":[16,23],"real":[18],"connected":[19],"Lie":[20],"group,":[21],"focusing":[22],"the":[24],"algebra":[25],"properties,":[26],"pointwise":[27],"multipliers,":[28],"localized":[29],"norms,":[30],"characterization":[32],"by":[33],"differences.":[34]},"counts_by_year":[{"year":2026,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-17T00:00:00"}