Riesz容量的Hausdorff测度和衰减率

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-04-29 DOI:10.1016/j.jmaa.2025.129625

Qiuling Fan, Richard S. Laugesen

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引用次数: 0

摘要

Riesz容量的衰减率随着指数的增加而产生Hausdorff测度。该结果适用于强可整流集，因此特别适用于欧氏空间的子流形。对于严格自相似分形，发现了一个单侧衰减估计。同时，给出了Riesz能量倒数的次可加性的一个纯测度理论证明。

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Hausdorff measure and decay rate of Riesz capacity

The decay rate of Riesz capacity as the exponent increases to the dimension of the set is shown to yield Hausdorff measure. The result applies to strongly rectifiable sets, and so in particular to submanifolds of Euclidean space. For strictly self-similar fractals, a one-sided decay estimate is found. Along the way, a purely measure theoretic proof is given for subadditivity of the reciprocal of Riesz energy.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.