{"id":"https://openalex.org/W7203917965","doi":"https://doi.org/10.48550/arxiv.2608.20266","title":"Necessary conditions for deterministic and stochastic maximal regularity","display_name":"Necessary conditions for deterministic and stochastic maximal regularity","publication_year":2026,"publication_date":"2026-08-20","ids":{"openalex":"https://openalex.org/W7203917965","doi":"https://doi.org/10.48550/arxiv.2608.20266"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.20266","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20266","pdf_url":"https://arxiv.org/pdf/2608.20266","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/2608.20266","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076485067","display_name":"Emiel Lorist","orcid":"https://orcid.org/0000-0002-2045-6035","observed_orcids":["https://orcid.org/0000-0002-2045-6035"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lorist, Emiel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069563754","display_name":"Jan van Neerven","orcid":"https://orcid.org/0000-0003-4577-7908","observed_orcids":["https://orcid.org/0000-0003-4577-7908"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"van Neerven, Jan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083145406","display_name":"Mark Veraar","orcid":"https://orcid.org/0000-0003-3167-7471","observed_orcids":["https://orcid.org/0000-0003-3167-7471"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Veraar, Mark","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113651131","display_name":"Lutz W. Weis","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weis, Lutz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T11545","display_name":"Advanced Banach Space Theory","score":0.8633000254631042,"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"}},"topics":[{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.8633000254631042,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.11879999935626984,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.0017000000225380063,"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/umd-banach-spaces","display_name":"UMD Banach spaces","score":0.9039999842643738},{"id":"https://openalex.org/keywords/r-boundedness","display_name":"R-boundedness","score":0.7630000114440918},{"id":"https://openalex.org/keywords/h-infinity-calculus","display_name":"H-infinity calculus","score":0.7900000214576721},{"id":"https://openalex.org/keywords/necessary-conditions","display_name":"necessary conditions","score":0.5759999752044678}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.852400004863739},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6575999855995178},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6202999949455261},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6134999990463257},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4957999885082245},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.47540000081062317},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.44279998540878296},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40700000524520874},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3977000117301941},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.38119998574256897},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.37220001220703125},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.35690000653266907},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3483999967575073},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.33320000767707825},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3325999975204468},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33059999346733093},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.31139999628067017},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.301800012588501},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2928999960422516},{"id":"https://openalex.org/C43494777","wikidata":"https://www.wikidata.org/wiki/Q1193403","display_name":"Regular space","level":3,"score":0.29100000858306885},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C176691602","wikidata":"https://www.wikidata.org/wiki/Q7097841","display_name":"Operator space","level":4,"score":0.2678000032901764}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.20266","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20266","pdf_url":"https://arxiv.org/pdf/2608.20266","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.2608.20266","doi":"https://doi.org/10.48550/arxiv.2608.20266","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.20266","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.20266","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20266","pdf_url":"https://arxiv.org/pdf/2608.20266","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/W7203917965.pdf","grobid_xml":"https://content.openalex.org/works/W7203917965.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4387322795"],"related_works":["https://openalex.org/W2796146001","https://openalex.org/W3010538354","https://openalex.org/W2008742060","https://openalex.org/W2014707464","https://openalex.org/W2280389320","https://openalex.org/W2011746797","https://openalex.org/W2950874560","https://openalex.org/W2078516184","https://openalex.org/W2144827466","https://openalex.org/W2036310445"],"abstract_inverted_index":{"We":[0,14],"study":[1,93],"the":[2,21,25,52,55,94,147,166],"role":[3],"of":[4,27,32,54,68,76,117],"Banach":[5,65,95],"space":[6,67,96,143],"geometry":[7,97],"in":[8,24,30],"deterministic":[9,48],"and":[10,47,158,163,173],"stochastic":[11,44,81,110],"maximal":[12,28,45,49,82],"regularity.":[13],"first":[15],"construct":[16],"an":[17,41,60,105],"example":[18],"showing":[19],"that":[20,71,122,155],"UMD":[22,64,114],"assumption":[23],"characterisation":[26],"$L^p$-regularity":[29,83],"terms":[31],"$R$-sectoriality":[33],"cannot":[34],"be":[35],"omitted.":[36],"Combining":[37],"this":[38,90,123],"construction":[39],"with":[40],"equivalence":[42],"between":[43],"regularity":[46,50],"on":[51,62,140,149],"$2$-concavification":[53],"underlying":[56,99],"space,":[57],"we":[58,92,120,153],"obtain":[59],"operator":[61],"a":[63,73,137,141,180],"function":[66],"type":[69,118],"$2$":[70],"has":[72],"bounded":[74],"$H^\\infty$-calculus":[75],"angle":[77],"zero,":[78],"but":[79,129],"fails":[80],"(SMR$_p$)":[84],"for":[85,109,132,145],"every":[86],"$p\\in[2,\\infty)$.":[87],"Motivated":[88],"by":[89],"example,":[91],"hypothesis":[98],"SMR$_p$":[100],"more":[101],"closely.":[102],"This":[103],"is":[104,125,177],"$R$-boundedness":[106],"condition":[107,124,169],"$(S_p)$":[108],"convolution":[111],"operators.":[112],"For":[113],"spaces":[115],"$X$":[116,176],"$2$,":[119],"show":[121],"not":[126],"only":[127,174],"sufficient,":[128],"also":[130],"necessary":[131],"two":[133],"canonical":[134],"test":[135],"operators:":[136],"diagonal":[138],"multiplier":[139],"Rademacher":[142],"and,":[144],"$q>2$,":[146],"Laplacian":[148],"$L^q(\\mathbb":[150],"R^d;X)$.":[151],"Finally,":[152],"prove":[154],"its":[156],"interval-kernel":[157],"exponential-kernel":[159],"formulations":[160],"are":[161],"equivalent":[162],"that,":[164],"at":[165],"endpoint":[167],"$p=2$,":[168],"$(S_2)$":[170],"holds":[171],"if":[172,175],"isomorphic":[178],"to":[179],"Hilbert":[181],"space.":[182]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-22T00:00:00"}