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16 - Applications in Functional Analysis

from Part Three - Applications

Published online by Cambridge University Press:  13 October 2020

Jonathan M. Fraser
Jonathan M. Fraser
Affiliation:
University of St Andrews, Scotland
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Summary

In thisfinal applications chapter, we consider a range of problems in functional and harmonic analysis. In Section 16.1 we begin with a well-established connection between the Assouad and lower dimensions and Hardy inequalities. In Section 16.2 we explore a problem involving maximal operators averaged over spheres, where the Assouad dimension plays a role in determining whether certain Lp-improving estimates are satisfied.

Keywords

Lp-spacemaximal functionHardy inequality
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Chapter
Information
Assouad Dimension and Fractal Geometry , pp. 230 - 236
Publisher: Cambridge University Press
Print publication year: 2020

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