{"id":"https://openalex.org/W7212035818","doi":"https://doi.org/10.48550/arxiv.2609.08193","title":"Fefferman--Stein type inequalities via area and maximal functions for Schr\u00f6dinger operators with applications","display_name":"Fefferman--Stein type inequalities via area and maximal functions for Schr\u00f6dinger operators with applications","publication_year":2026,"publication_date":"2026-09-08","ids":{"openalex":"https://openalex.org/W7212035818","doi":"https://doi.org/10.48550/arxiv.2609.08193"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.08193","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08193","pdf_url":"https://arxiv.org/pdf/2609.08193","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/2609.08193","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5150977867","display_name":"Ji Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Ji","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101415293","display_name":"Wanjun Li","orcid":"https://orcid.org/0000-0002-7700-6203","observed_orcids":["https://orcid.org/0000-0002-7700-6203"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Wanjun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5150916442","display_name":"Liang Song","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Song, Liang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100308452","display_name":"Lixin Yan","orcid":"https://orcid.org/0009-0005-5547-0047","observed_orcids":["https://orcid.org/0009-0005-5547-0047"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan, Lixin","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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9994999766349792,"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":0.9994999766349792,"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":0.0003000000142492354,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0,"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/fefferman-stein-inequality","display_name":"Fefferman-Stein inequality","score":0.9739999771118164},{"id":"https://openalex.org/keywords/area-function","display_name":"area function","score":0.843999981880188},{"id":"https://openalex.org/keywords/non-tangential-maximal-function","display_name":"non-tangential maximal function","score":0.9959999918937683},{"id":"https://openalex.org/keywords/schrodinger-operators","display_name":"Schr\u00f6dinger operators","score":0.8970000147819519},{"id":"https://openalex.org/keywords/stratified-lie-groups","display_name":"stratified Lie groups","score":0.9919999837875366},{"id":"https://openalex.org/keywords/sub-laplacian","display_name":"sub-Laplacian","score":0.9800000190734863},{"id":"https://openalex.org/keywords/atomic-decomposition","display_name":"atomic decomposition","score":0.8140000104904175},{"id":"https://openalex.org/keywords/riesz-transforms","display_name":"Riesz transforms","score":0.953000009059906}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8788999915122986},{"id":"https://openalex.org/C3018319951","wikidata":"https://www.wikidata.org/wiki/Q6795639","display_name":"Maximal operator","level":3,"score":0.6116999983787537},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.580299973487854},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5733000040054321},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5065000057220459},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.44999998807907104},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4260999858379364},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4185999929904938},{"id":"https://openalex.org/C188422159","wikidata":"https://www.wikidata.org/wiki/Q6795639","display_name":"Maximal function","level":2,"score":0.38830000162124634},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.37940001487731934},{"id":"https://openalex.org/C184701930","wikidata":"https://www.wikidata.org/wiki/Q190546","display_name":"Cauchy\u2013Schwarz inequality","level":3,"score":0.37790000438690186},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.3765000104904175},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.375},{"id":"https://openalex.org/C65630602","wikidata":"https://www.wikidata.org/wiki/Q2278680","display_name":"Shift operator","level":4,"score":0.37130001187324524},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.3612000048160553},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3531999886035919},{"id":"https://openalex.org/C83295520","wikidata":"https://www.wikidata.org/wiki/Q1318586","display_name":"Locally integrable function","level":3,"score":0.34470000863075256},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3375999927520752},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33719998598098755},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.3239000141620636},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.31119999289512634},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C75413324","wikidata":"https://www.wikidata.org/wiki/Q1530791","display_name":"Square-integrable function","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.2994999885559082},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C82916341","wikidata":"https://www.wikidata.org/wiki/Q6934990","display_name":"Multiplication operator","level":3,"score":0.2831000089645386},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.2614000141620636}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.08193","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08193","pdf_url":"https://arxiv.org/pdf/2609.08193","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.2609.08193","doi":"https://doi.org/10.48550/arxiv.2609.08193","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.08193","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:2609.08193","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08193","pdf_url":"https://arxiv.org/pdf/2609.08193","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/G1704823527","display_name":null,"funder_award_id":"12471097","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6760170314","display_name":null,"funder_award_id":"12571111","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212035818.pdf","grobid_xml":"https://content.openalex.org/works/W7212035818.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3045245007","https://openalex.org/W7072045592","https://openalex.org/W2898366959","https://openalex.org/W1963604032","https://openalex.org/W4400888992","https://openalex.org/W1997353965","https://openalex.org/W2768363217","https://openalex.org/W7125508770","https://openalex.org/W4406847944","https://openalex.org/W2155333461"],"abstract_inverted_index":{"In":[0],"this":[1,53],"paper,":[2],"we":[3,51,93],"establish":[4],"a":[5,43],"Fefferman--Stein":[6],"inequality":[7,54],"in":[8,80],"terms":[9],"of":[10,64,124,132],"area":[11,101],"function":[12,16],"and":[13,40,69,104,126],"non-tangential":[14],"maximal":[15],"associated":[17,73,108],"with":[18,74,109,135],"the":[19,35,56,75,81,100,105,110,121,130],"Schr\u00f6dinger":[20,76,111],"operator":[21,77,103,112],"$\\mathcal{L}":[22],"=":[23],"-\u0394+":[24],"V$":[25],"on":[26,37,113],"stratified":[27,66],"Lie":[28,67],"groups":[29,68],"$\\mathcal":[30,38,59],"G$,":[31],"where":[32],"$\u0394$":[33],"denotes":[34],"sub-Laplacian":[36],"G$":[39],"$V$":[41],"is":[42],"nonnegative":[44],"locally":[45],"integrable":[46],"function.":[47],"As":[48],"an":[49],"application,":[50],"extend":[52],"to":[55,129],"tensor":[57],"product":[58],"G_1":[60,85,115],"\\times":[61,86,116],"\\mathcal":[62,87,117],"G_2$":[63],"two":[65],"develop":[70],"atomic":[71,91],"decompositions":[72],"for":[78,99],"functions":[79],"Orlicz":[82],"space":[83],"$L\\log^{+}L(\\mathcal":[84,114],"G_2).$":[88],"Using":[89],"these":[90],"decompositions,":[92],"further":[94],"prove":[95],"weak-type":[96],"endpoint":[97],"estimates":[98],"integral":[102],"Riesz":[106],"transforms":[107],"G_2),$":[118],"thereby":[119],"extending":[120],"celebrated":[122],"result":[123],"R.\\,Fefferman":[125],"E.M.\\,Stein":[127],"\\cite{FSt1982}":[128],"setting":[131],"singular":[133],"integrals":[134],"non-smooth":[136],"kernels.":[137]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-10T00:00:00"}