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

Ángel Arroyo, José G. Llorente

Research output: Contribution to journalArticleResearch

Abstract

c 2019 American Mathematical Society A metric measure space (X, d, μ) is said to satisfy the strong annular decay condition if there is a constant C > 0 such that μ(B(x, R) \ B(x, r)) ≤ C RR− r μ(B(x, R)) for each x ∈ X and all 0 < r ≤ R. If d∞ is the distance induced by the ∞-norm in RN, we construct examples of singular measures μ on RN such that (RN , d∞, μ) satisfies the strong annular decay condition.
Original languageEnglish
Pages (from-to)4409-4423
Number of pages15
JournalProceedings of the American Mathematical Society
Volume147
Issue number10
DOIs
Publication statusPublished - 17 May 2019

Keywords

  • Annular decay condition
  • Bernoulli product
  • PROPERTY
  • REGULARITY
  • REVERSE HOLDER CLASSES
  • THEOREMS
  • doubling measure
  • metric measure space

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