{"title":"A metric counterpart of the Gu-Yung formula.","authors":"Stefano Buccheri, Wojciech Górny","doi":"10.1007/s13163-025-00554-4","DOIUrl":"10.1007/s13163-025-00554-4","url":null,"abstract":"<p><p>In this note we consider a generalisation to the metric setting of the recent work (Gu and Yung in J Funct Anal 281:109075, 2021). In particular, we show that under relatively weak conditions on a metric measure space <math><mrow><mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>d</mi> <mo>,</mo> <mi>ν</mi> <mo>)</mo></mrow> </math> , it holds true that <dispformula> <math> <mrow><mrow><mo>[</mo></mrow> <mfrac><mrow><mi>u</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>-</mo> <mi>u</mi> <mo>(</mo> <mi>y</mi> <mo>)</mo></mrow> <mrow><mi>d</mi> <msup><mrow><mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo></mrow> <mfrac><mi>s</mi> <mi>p</mi></mfrac> </msup> </mrow> </mfrac> <msub><mrow><mo>]</mo></mrow> <mrow><msubsup><mi>L</mi> <mi>w</mi> <mi>p</mi></msubsup> <mrow><mo>(</mo> <mi>X</mi> <mo>×</mo> <mi>X</mi> <mo>,</mo> <mi>ν</mi> <mo>⊗</mo> <mi>ν</mi> <mo>)</mo></mrow> </mrow> </msub> <mo>≈</mo> <msub><mrow><mo>‖</mo> <mi>u</mi> <mo>‖</mo></mrow> <mrow><msup><mi>L</mi> <mi>p</mi></msup> <mrow><mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>ν</mi> <mo>)</mo></mrow> </mrow> </msub> <mo>,</mo></mrow> </math> </dispformula> where <i>s</i> is a generalised dimension associated to <i>X</i> and <math> <msub><mrow><mo>[</mo> <mo>·</mo> <mo>]</mo></mrow> <msubsup><mi>L</mi> <mi>w</mi> <mi>p</mi></msubsup> </msub> </math> is the weak Lebesgue norm. We provide some counterexamples which show that our assumptions are optimal.</p>","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":"39 3","pages":"695-720"},"PeriodicalIF":1.4,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13457237/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148714325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ranks of maps of vector bundles","authors":"Montserrat Teixidor i bigas","doi":"10.1007/s13163-023-00477-y","DOIUrl":"https://doi.org/10.1007/s13163-023-00477-y","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42154172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Strict $${mathcal {C}}^p$$-triangulations of sets locally definable in o-minimal structures with an application to a $$mathcal C^p$$-approximation problem","authors":"W. Pawłucki","doi":"10.1007/s13163-023-00471-4","DOIUrl":"https://doi.org/10.1007/s13163-023-00471-4","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42972006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Terracini loci of curves","authors":"E. Ballico, L. Chiantini","doi":"10.1007/s13163-023-00467-0","DOIUrl":"https://doi.org/10.1007/s13163-023-00467-0","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41872393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algebraic valuation ring extensions as limits of complete intersection algebras","authors":"D. Popescu","doi":"10.1007/s13163-023-00468-z","DOIUrl":"https://doi.org/10.1007/s13163-023-00468-z","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48050341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction: On the Michor?Mumford phenomenon in the infinite dimensional Heisenberg group","authors":"Valentino Magnani, Daniele Tiberio","doi":"10.1007/s13163-023-00463-4","DOIUrl":"https://doi.org/10.1007/s13163-023-00463-4","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":" ","pages":"1"},"PeriodicalIF":0.8,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46585310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction to: Some q-supercongruences from the Gasper and Rahman quadratic summation","authors":"Victor J. W. Guo","doi":"10.1007/s13163-023-00456-3","DOIUrl":"https://doi.org/10.1007/s13163-023-00456-3","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":"1 1","pages":"1"},"PeriodicalIF":0.8,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46241884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Critical metrics for quadratic curvature functionals on some solvmanifolds","authors":"G. Calvaruso, A. Zaeim","doi":"10.1007/s13163-022-00448-9","DOIUrl":"https://doi.org/10.1007/s13163-022-00448-9","url":null,"abstract":"","PeriodicalId":49605,"journal":{"name":"Revista Matematica Complutense","volume":"1 1","pages":"1-18"},"PeriodicalIF":0.8,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44574949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}