{"id":"https://openalex.org/W7214736106","doi":"https://doi.org/10.48550/arxiv.2609.34331","title":"Riesz transform on eventually Gaussian local trees","display_name":"Riesz transform on eventually Gaussian local trees","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214736106","doi":"https://doi.org/10.48550/arxiv.2609.34331"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.34331","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34331","pdf_url":"https://arxiv.org/pdf/2609.34331","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/2609.34331","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050804243","display_name":"Fabrice Baudoin","orcid":"https://orcid.org/0000-0001-5645-1060","observed_orcids":["https://orcid.org/0000-0001-5645-1060"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Baudoin, Fabrice","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153416177","display_name":"Aobo Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Aobo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5153437544","display_name":"Li Chen","orcid":"https://orcid.org/0000-0002-0335-466X","observed_orcids":["https://orcid.org/0000-0002-0335-466X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Li","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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.8345000147819519,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.8345000147819519,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.14890000224113464,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.002400000113993883,"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/riesz-transforms","display_name":"Riesz transforms","score":0.9990000128746033},{"id":"https://openalex.org/keywords/metric-measure-spaces","display_name":"metric measure spaces","score":0.6930000185966492},{"id":"https://openalex.org/keywords/dirichlet-forms","display_name":"Dirichlet forms","score":0.8690000176429749},{"id":"https://openalex.org/keywords/heat-kernel-estimates","display_name":"heat kernel estimates","score":0.824999988079071},{"id":"https://openalex.org/keywords/reverse-holder-inequality","display_name":"reverse H\u00f6lder inequality","score":0.6520000100135803},{"id":"https://openalex.org/keywords/dini-condition","display_name":"Dini condition","score":0.7390000224113464},{"id":"https://openalex.org/keywords/scale-function","display_name":"scale function","score":0.6610000133514404},{"id":"https://openalex.org/keywords/harmonic-functions","display_name":"harmonic functions","score":0.5180000066757202},{"id":"https://openalex.org/keywords/geometric-group-actions","display_name":"geometric group actions","score":0.593999981880188}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9203000068664551},{"id":"https://openalex.org/C82997116","wikidata":"https://www.wikidata.org/wiki/Q7333169","display_name":"Riesz transform","level":2,"score":0.6450999975204468},{"id":"https://openalex.org/C189987565","wikidata":"https://www.wikidata.org/wiki/Q7333166","display_name":"Riesz potential","level":2,"score":0.6248000264167786},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6054999828338623},{"id":"https://openalex.org/C183212220","wikidata":"https://www.wikidata.org/wiki/Q3345669","display_name":"Heat kernel","level":2,"score":0.5778999924659729},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5680000185966492},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5676000118255615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5376999974250793},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.5339000225067139},{"id":"https://openalex.org/C2778872062","wikidata":"https://www.wikidata.org/wiki/Q5280765","display_name":"Dirichlet form","level":4,"score":0.5060999989509583},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.46860000491142273},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.44850000739097595},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4406000077724457},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4383000135421753},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4343999922275543},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.397599995136261},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.36800000071525574},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.36039999127388},{"id":"https://openalex.org/C2781362121","wikidata":"https://www.wikidata.org/wiki/Q7631785","display_name":"Subordinator","level":3,"score":0.3549000024795532},{"id":"https://openalex.org/C8464174","wikidata":"https://www.wikidata.org/wiki/Q868279","display_name":"Harnack's inequality","level":2,"score":0.33410000801086426},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.31380000710487366},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C164506360","wikidata":"https://www.wikidata.org/wiki/Q1751496","display_name":"Poincar\u00e9 inequality","level":3,"score":0.2879999876022339},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.2784999907016754},{"id":"https://openalex.org/C188422159","wikidata":"https://www.wikidata.org/wiki/Q6795639","display_name":"Maximal function","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C56969512","wikidata":"https://www.wikidata.org/wiki/Q3527217","display_name":"M. Riesz extension theorem","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C91558832","wikidata":"https://www.wikidata.org/wiki/Q731894","display_name":"H\u00f6lder's inequality","level":4,"score":0.2703999876976013},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C185644265","wikidata":"https://www.wikidata.org/wiki/Q3711848","display_name":"Sobolev inequality","level":3,"score":0.2660999894142151},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.2597000002861023},{"id":"https://openalex.org/C163072092","wikidata":"https://www.wikidata.org/wiki/Q1135706","display_name":"Harnack's principle","level":3,"score":0.2540000081062317},{"id":"https://openalex.org/C113675457","wikidata":"https://www.wikidata.org/wiki/Q1357684","display_name":"Riesz representation theorem","level":2,"score":0.2508000135421753},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.25}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.34331","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34331","pdf_url":"https://arxiv.org/pdf/2609.34331","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.2609.34331","doi":"https://doi.org/10.48550/arxiv.2609.34331","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.34331","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:2609.34331","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34331","pdf_url":"https://arxiv.org/pdf/2609.34331","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":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214736106.pdf","grobid_xml":"https://content.openalex.org/works/W7214736106.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2069359224","https://openalex.org/W4404349661","https://openalex.org/W4415199738","https://openalex.org/W7214007750"],"related_works":["https://openalex.org/W2952101686","https://openalex.org/W1854573896","https://openalex.org/W2098474757","https://openalex.org/W1970067922","https://openalex.org/W4309803813","https://openalex.org/W7099881575","https://openalex.org/W7118130708","https://openalex.org/W2762963759","https://openalex.org/W2274799773","https://openalex.org/W2626301650"],"abstract_inverted_index":{"We":[0,146],"study":[1],"the":[2,29,41,64,90,101,115,138,157,180,189,196],"Riesz":[3,117,132,197,200],"transform":[4],"$\\mathcal{R}=\\partial(-\u0394)^{-\\frac{1}{2}}$":[5],"on":[6,100,108],"uniform":[7,77],"local":[8,97],"trees,":[9],"metric":[10],"measure":[11,33,43],"spaces":[12,165],"that":[13,95,148],"are":[14],"locally":[15],"real":[16],"trees":[17],"and":[18,61,71,84,113,160,198],"whose":[19,171],"canonical":[20],"Dirichlet":[21],"form":[22],"is":[23,50,66],"built":[24],"from":[25,52],"weak":[26],"derivatives":[27],"along":[28],"skeleton.":[30],"The":[31],"reference":[32],"$m$":[34],"may":[35],"be":[36,141],"singular":[37],"with":[38,58],"respect":[39],"to":[40,54,140],"length":[42],"$\u03bd$,":[44],"so":[45],"boundedness":[46,105,123],"of":[47,106,124,192],"$\\mathcal":[48],"R$":[49],"understood":[51],"$L^{p}(m)$":[53],"$L^{p}(\u03bd)$.":[55],"In":[56],"contrast":[57],"fractal-like":[59],"manifolds":[60],"cable":[62],"systems,":[63],"diffusion":[65],"sub-Gaussian":[67],"at":[68,73,143],"small":[69,144],"scales":[70],"Gaussian":[72],"large":[74],"scales.":[75,145],"Under":[76],"volume":[78],"growth,":[79],"two-sided":[80],"heat":[81,91],"kernel":[82],"estimates":[83],"a":[85,96,130,149,167],"pointwise":[86],"gradient":[87,158],"estimate":[88],"for":[89,110,119,126,134,153,164,179,194],"kernel,":[92],"we":[93,187],"prove":[94],"Dini":[98],"condition":[99],"scale":[102],"function":[103],"implies":[104],"$\\mathcal{R}$":[107,125],"$L^{p}$":[109],"every":[111,120],"$p\\in[2,\\infty)$,":[112],"hence":[114],"reverse":[116,131,150,199],"inequality":[118,133,152],"$p\\in(1,2]$.":[121],"Conversely,":[122],"some":[127,135],"$p<2$,":[128],"or":[129],"$p>2$,":[136],"forces":[137],"space":[139],"one-dimensional":[142],"show":[147],"H\u00f6lder":[151],"harmonic":[154],"functions":[155],"yields":[156],"estimate,":[159],"verify":[161],"all":[162],"hypotheses":[163],"carrying":[166],"geometric":[168],"group":[169],"action":[170],"generators":[172],"have":[173],"bounded":[174],"displacement.":[175],"As":[176],"an":[177],"application,":[178],"alternating":[181],"Vicsek":[182],"fractafold":[183],"in":[184],"$\\mathbb":[185],"Z^{d}$":[186],"determine":[188],"exact":[190],"ranges":[191],"$p$":[193],"which":[195],"inequalities":[201],"hold.":[202]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}