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arXiv · 1808.07669

On a class of singular measures satisfying a strong annular decay condition

Ángel Arroyo·José G. Llorente
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Abstract

A metric measure space $(X,d,\mu)$ is said to satisfy the strong annular decay condition if there is a constant $C>0$ such that $$ \mu\big(B(x,R)\setminus B(x,r)\big)\leq C\, \frac{R-r}{R}\, \mu (B(x,R)) $$ for each $x\in X$ and all $0<r \leq R$. If $d_{\infty}$ is the distance induced by the $\infty$-norm in $\mathbb{R}^N$, we construct examples of singular measures $\mu$ on $\mathbb{R}^N$ such that $(\mathbb{R}^N, d_{\infty},\mu)$ satisfies the strong annular decay condition.

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Ángel Arroyo, José G. Llorente. 2018-08-23. On a class of singular measures satisfying a strong annular decay condition. https://arxiv.org/abs/1808.07669

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