Assouad Type Dimensions in Geometric Analysis
Lehrbäck, J. (2021). Assouad Type Dimensions in Geometric Analysis. In U. Freiberg, B. Hambly, M. Hinz, & S. Winter (Eds.), Fractal Geometry and Stochastics VI (pp. 25-46). Birkhäuser. Progress in Probability, 76. https://doi.org/10.1007/978-3-030-59649-1_2
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Progress in ProbabilityAuthors
Date
2021Discipline
MatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis and Dynamics Research (Centre of Excellence)Copyright
© Springer Nature Switzerland AG 2021
We consider applications of the dual pair of the (upper) Assouad dimension and the lower (Assouad) dimension in analysis. We relate these notions to other dimensional conditions such as a Hausdorff content density condition and an integrability condition for the distance function. The latter condition leads to a characterization of the Muckenhoupt Ap properties of distance functions in terms of the (upper) Assouad dimension. It is also possible to give natural formulations for the validity of Hardy–Sobolev inequalities using these dual Assouad dimensions, and this helps to understand the previously observed dual nature of certain cases of these inequalities.
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BirkhäuserParent publication ISBN
978-3-030-59648-4Conference
International Conference on Fractal Geometry and StochasticsIs part of publication
Fractal Geometry and Stochastics VIISSN Search the Publication Forum
1050-6977Keywords
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https://converis.jyu.fi/converis/portal/detail/Publication/52590230
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