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Lehrbäck, Juha; Tuominen, Heli

A note on the dimensions of Assouad and Aikawa. (English) Zbl 1279.54022

J. Math. Soc. Japan 65, No. 2, 343-356 (2013).
Authors’ abstract: We show that in Euclidean space and other regular metric spaces, the notions of dimensions defined by Assouad and Aikawa coincide. In addition, in more general metric spaces, we study the relationship between these two dimensions and a related codimension and give an application of the Aikawa (co)dimension for the Hardy inequalities.
Reviewer: M. G. Charalambous (Samos)

Cited in 21 Documents

MSC:

54F45 Dimension theory in general topology
28A12 Contents, measures, outer measures, capacities
54E35 Metric spaces, metrizability
26D15 Inequalities for sums, series and integrals

Keywords:

Assouad dimension; Aikawa dimension; metric space; doubling measure; Hardy inequality
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\textit{J. Lehrbäck} and \textit{H. Tuominen}, J. Math. Soc. Japan 65, No. 2, 343--356 (2013; Zbl 1279.54022)
Full Text: DOI Euclid

References:

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