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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a class of singular measures satisfying a strong annular decay condition
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by Ángel Arroyo and José G. Llorente PDF
Proc. Amer. Math. Soc. 147 (2019), 4409-4423 Request permission

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 \begin{equation*} \mu \big ( B(x, R) \setminus B(x,r) \big ) \leq C \frac {R-r}{R} \mu (B(x,R)) \end{equation*} 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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Additional Information
  • Ángel Arroyo
  • Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FI-40014 Jyväskylä, Finland
  • Email: angel.a.arroyo@jyu.fi
  • José G. Llorente
  • Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
  • MR Author ID: 327617
  • Email: jgllorente@mat.uab.cat
  • Received by editor(s): September 4, 2018
  • Received by editor(s) in revised form: January 25, 2019
  • Published electronically: May 17, 2019
  • Additional Notes: This research was partially supported by grants MTM2017-85666-P, 2017 SGR 395.
  • Communicated by: Jeremy Tyson
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4409-4423
  • MSC (2010): Primary 28A75, 30L99
  • DOI: https://doi.org/10.1090/proc/14576
  • MathSciNet review: 4002552