图上的Poincaré不等式

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2023-03-31 DOI:10.1007/s10476-023-0215-5

M. Levi, F. Santagati, A. Tabacco, M. Vallarino

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引用次数: 2

摘要

每个具有计数测度的有界度图都满足Lp-Poincaré不等式的局部形式，p∈[1，∞]。我们证明了在树图上，庞加莱常数至少随球半径呈指数增长。另一方面，我们证明，令人惊讶的是，赋予流量测度的树支持Lp-Poincaré不等式的全局版本，尽管它们是指数增长的非加倍测度。

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Poincaré inequalities on graphs

Every graph of bounded degree endowed with the counting measure satisfies a local version of L^p-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 L^p-Poincaré inequality, despite the fact that they are nondoubling measures of exponential growth.

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

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.