Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
A note on the dimensions of Assouad and Aikawa
Juha Lehrbäck, Heli Tuominen
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Keywords: Assouad dimension, Aikawa dimension, metric space, doubling measure, Hardy inequality
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2013 Volume 65 Issue 2 Pages 343-356

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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.
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© 2013 The Mathematical Society of Japan
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