{"id":"https://openalex.org/W7223064083","doi":"https://doi.org/10.48550/arxiv.2610.24201","title":"Diamond Maximal Operators: Classification, Moduli, and Oscillation Envelopes","display_name":"Diamond Maximal Operators: Classification, Moduli, and Oscillation Envelopes","publication_year":2026,"publication_date":"2026-10-16","ids":{"openalex":"https://openalex.org/W7223064083","doi":"https://doi.org/10.48550/arxiv.2610.24201"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.24201","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24201","pdf_url":"https://arxiv.org/pdf/2610.24201","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/2610.24201","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114655531","display_name":"Mohammadreza Mohajer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I10213569","display_name":"Cape Breton University","ror":"https://ror.org/052y05165","country_code":"CA","type":"education","lineage":["https://openalex.org/I10213569"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Mohajer, Mohammadreza","raw_affiliation_strings":["Department of Mathematics, Physics and Geology , Cape Breton University , 1250 Grand Lake Road , Sydney , NS B1P 6L2 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Physics and Geology , Cape Breton University , 1250 Grand Lake Road , Sydney , NS B1P 6L2 , Canada","institution_ids":["https://openalex.org/I10213569"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5114655531"],"corresponding_institution_ids":["https://openalex.org/I10213569"],"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":0.9984999895095825,"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":0.9984999895095825,"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":0.0005000000237487257,"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":0.00019999999494757503,"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/maximal-functions","display_name":"maximal operators","score":0.9580000042915344},{"id":"https://openalex.org/keywords/non-archimedean-local-fields","display_name":"non-archimedean local fields","score":0.875},{"id":"https://openalex.org/keywords/finite-fourier-transform","display_name":"finite Fourier transform","score":0.8169999718666077},{"id":"https://openalex.org/keywords/grassmannians","display_name":"Grassmannians","score":0.5559999942779541}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8984000086784363},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5509999990463257},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5216000080108643},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.4796000123023987},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.3865000009536743},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3853999972343445},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.38100001215934753},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C2779638872","wikidata":"https://www.wikidata.org/wiki/Q10942247","display_name":"Resolution of singularities","level":3,"score":0.3537999987602234},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C188422159","wikidata":"https://www.wikidata.org/wiki/Q6795639","display_name":"Maximal function","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.32260000705718994},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.32170000672340393},{"id":"https://openalex.org/C28799612","wikidata":"https://www.wikidata.org/wiki/Q685437","display_name":"Hilbert transform","level":3,"score":0.31859999895095825},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.31349998712539673},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.305400013923645},{"id":"https://openalex.org/C27156116","wikidata":"https://www.wikidata.org/wiki/Q1778098","display_name":"Pointwise convergence","level":3,"score":0.30219998955726624},{"id":"https://openalex.org/C102205669","wikidata":"https://www.wikidata.org/wiki/Q191690","display_name":"Partition of unity","level":3,"score":0.2915000021457672},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C183212220","wikidata":"https://www.wikidata.org/wiki/Q3345669","display_name":"Heat kernel","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.271699994802475},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2703000009059906},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2694999873638153},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.2623000144958496},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.2583000063896179}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.24201","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24201","pdf_url":"https://arxiv.org/pdf/2610.24201","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.2610.24201","doi":"https://doi.org/10.48550/arxiv.2610.24201","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.24201","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:2610.24201","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24201","pdf_url":"https://arxiv.org/pdf/2610.24201","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223064083.pdf","grobid_xml":"https://content.openalex.org/works/W7223064083.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1528337088","https://openalex.org/W1978372982","https://openalex.org/W2001657683","https://openalex.org/W2064663265","https://openalex.org/W2094683997","https://openalex.org/W2163743987","https://openalex.org/W2480965565","https://openalex.org/W2801721719","https://openalex.org/W4247556508","https://openalex.org/W4248262852","https://openalex.org/W7161681338"],"related_works":["https://openalex.org/W3148578922","https://openalex.org/W2259922017","https://openalex.org/W752148168","https://openalex.org/W7099246800","https://openalex.org/W1968624893","https://openalex.org/W14414870","https://openalex.org/W2379005429","https://openalex.org/W3146765165","https://openalex.org/W4416875653","https://openalex.org/W3085785219"],"abstract_inverted_index":{"We":[0,176],"study":[1],"maximal":[2,39,128],"averages":[3],"generated":[4],"by":[5,155,169,192],"bounded":[6,149,183],"cancellative":[7,184],"kernels":[8,67,137,147,185],"taking":[9],"values":[10],"in":[11,22],"finite-dimensional":[12],"real":[13],"normed":[14],"spaces,":[15],"on":[16,20,69,148],"Euclidean":[17],"balls":[18,21],"and":[19,93,116,140,194,217,242],"a":[23,28,70,122],"non-Archimedean":[24],"local":[25,189],"field":[26,239],"with":[27,50,163,165,186],"fixed":[29,71],"uniformizer.":[30],"For":[31,65,101,143],"angular":[32,47,57,66],"kernels,":[33,103],"pointwise":[34],"domination":[35,152],"of":[36,45,75,108,125,135,159,173,198,208,236],"the":[37,51,76,104,109,117,126,156,170,178,187,202,206,209,214,218,227,237,243,246],"full":[38,127],"operators":[40],"is":[41,121,153,224,240],"equivalent":[42,225],"to":[43,226],"factorization":[44],"their":[46],"averaging":[48,110],"maps,":[49],"same":[52],"optimal":[53,166,247],"constant.":[54],"Nonzero":[55],"scalar":[56],"comparison":[58,248],"classes":[59,89],"are":[60],"therefore":[61],"projective":[62],"kernel":[63],"classes.":[64],"constant":[68],"finite":[72,210],"measurable":[73],"partition":[74],"direction":[77],"space,":[78],"symmetric":[79],"convex":[80,106],"bodies":[81],"classify":[82,98,213],"exact":[83],"norm":[84],"measurements,":[85],"Grassmannians":[86],"parametrize":[87],"nonzero":[88,144],"under":[90],"mutual":[91,151],"domination,":[92],"positive":[94],"semidefinite":[95],"Gram":[96],"matrices":[97],"Hilbert-valued":[99],"measurements.":[100],"general":[102],"closed":[105],"hull":[107],"densities":[111],"obtained":[112],"from":[113],"all":[114,181],"scales":[115],"dual":[118],"unit":[119],"ball":[120],"complete":[123],"invariant":[124],"operator.":[129],"A":[130],"dilation":[131],"example":[132],"exhibits":[133],"identifications":[134],"residue":[136,146,199,238],"beyond":[138],"scaling":[139],"unit-coordinate":[141],"changes.":[142],"radial":[145],"inputs,":[150],"classified":[154],"unit-circle":[157],"zeros":[158],"filter":[160],"polynomials,":[161],"counted":[162],"multiplicity,":[164],"constants":[167,193],"given":[168],"$\\ell^1$":[171],"norms":[172],"convolution":[174],"quotients.":[175],"identify":[177],"envelope":[179],"over":[180],"normalized":[182],"best":[188],"$L^1$":[190],"approximation":[191],"prove":[195],"quantitative":[196],"convergence":[197],"envelopes":[200],"as":[201],"resolution":[203],"increases.":[204],"Finally,":[205],"weights":[207,244],"Fourier":[211],"transform":[212],"one-level":[215],"energy":[216],"associated":[219],"Carleson":[220],"functional.":[221],"This":[222],"functional":[223],"$BMO_2$":[228],"seminorm":[229],"precisely":[230],"when":[231],"every":[232],"nontrivial":[233],"additive":[234],"character":[235],"detected,":[241],"determine":[245],"constants.":[249]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}