A4 Article in conference proceedings
Assouad Type Dimensions in Geometric Analysis (2021)
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
JYU authors or editors
Publication details
All authors or editors: Lehrbäck, Juha
Parent publication: Fractal Geometry and Stochastics VI
Parent publication editors: Freiberg, Uta; Hambly, Ben; Hinz, Michael; Winter, Steffen
Conference:
- International Conference on Fractal Geometry and Stochastics
Place and date of conference: Bad Herrenalb, Germany, 30.9.-5.10.2018
ISBN: 978-3-030-59648-4
eISBN: 978-3-030-59649-1
Journal or series: Progress in Probability
ISSN: 1050-6977
eISSN: 2297-0428
Publication year: 2021
Number in series: 76
Pages range: 25-46
Number of pages in the book: 307
Publisher: Birkhäuser
Place of Publication: Cham
Publication country: Switzerland
Publication language: English
DOI: https://doi.org/10.1007/978-3-030-59649-1_2
Publication open access: Not open
Publication channel open access:
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/75072
Abstract
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.
Keywords: measure theory; partial differential equations; inequalities (mathematics)
Free keywords: Assouad dimension; Lower dimension; Aikawa condition; Muckenhoupt weight; Hardy–Sobolev inequality
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2021
JUFO rating: 1
