{"title":"图上的Poincaré不等式","authors":"M. Levi, F. Santagati, A. Tabacco, M. Vallarino","doi":"10.1007/s10476-023-0215-5","DOIUrl":null,"url":null,"abstract":"<div><p>Every graph of bounded degree endowed with the counting measure satisfies a local version of <i>L</i><sup><i>p</i></sup>-Poincaré inequality, <i>p ∈</i> [1, ∞]. We show that on graphs which are trees the Poincaré constant grows at least exponentially with the radius of balls. On the other hand, we prove that, surprisingly, trees endowed with a flow measure support a global version of <i>L</i><sup><i>p</i></sup>-Poincaré inequality, despite the fact that they are nondoubling measures of exponential growth.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 2","pages":"529 - 544"},"PeriodicalIF":0.6000,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Poincaré inequalities on graphs\",\"authors\":\"M. Levi, F. Santagati, A. Tabacco, M. Vallarino\",\"doi\":\"10.1007/s10476-023-0215-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Every graph of bounded degree endowed with the counting measure satisfies a local version of <i>L</i><sup><i>p</i></sup>-Poincaré inequality, <i>p ∈</i> [1, ∞]. We show that on graphs which are trees the Poincaré constant grows at least exponentially with the radius of balls. On the other hand, we prove that, surprisingly, trees endowed with a flow measure support a global version of <i>L</i><sup><i>p</i></sup>-Poincaré inequality, despite the fact that they are nondoubling measures of exponential growth.</p></div>\",\"PeriodicalId\":55518,\"journal\":{\"name\":\"Analysis Mathematica\",\"volume\":\"49 2\",\"pages\":\"529 - 544\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-03-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10476-023-0215-5\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis Mathematica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-023-0215-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Every graph of bounded degree endowed with the counting measure satisfies a local version of Lp-Poincaré inequality, p ∈ [1, ∞]. We show that on graphs which are trees the Poincaré constant grows at least exponentially with the radius of balls. On the other hand, we prove that, surprisingly, trees endowed with a flow measure support a global version of Lp-Poincaré inequality, despite the fact that they are nondoubling measures of exponential growth.
期刊介绍：
Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx).
The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx).
The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.
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