Measures satisfying a refined doubling condition and absolute continuity
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- by Alf Jonsson PDF
- Proc. Amer. Math. Soc. 123 (1995), 2441-2446 Request permission
Abstract:
It is shown that for certain subsets $F \subset {\mathbb {R}^n}$, two measures with support F satisfying a refined doubling condition are necessarily mutually absolutely continuous. This is contrary to the situation with measures satisfying the usual doubling condition, in which case no such result is available.References
- A. S. Besicovitch, A general form of the covering principle and relative differentiation of additive functions, Proc. Cambridge Philos. Soc. 41 (1945), 103–110. MR 12325, DOI 10.1017/s0305004100022453
- Alf Jonsson, Besov spaces on closed subsets of $\textbf {R}^n$, Trans. Amer. Math. Soc. 341 (1994), no. 1, 355–370. MR 1132434, DOI 10.1090/S0002-9947-1994-1132434-6
- Alf Jonsson and Hans Wallin, Function spaces on subsets of $\textbf {R}^n$, Math. Rep. 2 (1984), no. 1, xiv+221. MR 820626
- A. L. Vol′berg and S. V. Konyagin, On measures with the doubling condition, Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987), no. 3, 666–675 (Russian); English transl., Math. USSR-Izv. 30 (1988), no. 3, 629–638. MR 903629
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2441-2446
- MSC: Primary 28A15
- DOI: https://doi.org/10.1090/S0002-9939-1995-1283554-3
- MathSciNet review: 1283554