On the existence of doubling measures with certain regularity properties

Author:

Bylund Per,Gudayol Jaume

Abstract

Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the pseudo-metric. Then we construct a doubling measure for which the measure of a dilated ball is closely related to these dimensions.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference8 articles.

1. Doctoral Thesis;Bylund, Per,1994

2. [Dyn] E. M. Dynkin, Free interpolation by functions with derivatives in 𝐻¹, J. Soviet Math. 27 (1984), 2475-2481.

3. [Gud] Jaume Gudayol, Boundary behaviour of functions in Hardy-Sobolev spaces, doctoral dissertation, Universitat de Barcelona, 1997.

4. Besov spaces on closed subsets of 𝑅ⁿ;Jonsson, Alf;Trans. Amer. Math. Soc.,1994

5. [J-W] Alf Jonsson and Hans Wallin, Function spaces on subsets of ℝⁿ, Math. Reports Volume 2, Part 1, Harwood Academics Publ. GmbH, 1984.

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