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RESEARCH PRODUCT

A note on the dimensions of Assouad and Aikawa

Heli TuominenJuha Lehrbäck

subject

Pure mathematicsAssouad dimensionEuclidean spaceGeneral Mathematicsmetric spaceDimension (graph theory)Mathematical analysista111CodimensionAikawa dimension54F4554E35Metric space26D15Hardy inequalitydoubling measureMathematics::Metric Geometry28A12Mathematics

description

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.

yearjournalcountryeditionlanguage
2013-04-01Journal of the Mathematical Society of Japan
10.2969/jmsj/06520343https://doi.org/10.2969/jmsj/06520343