On the $L^q$-dimensions of measures on Hueter-Lalley type self-affine sets
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- by Jonathan M. Fraser and Tom Kempton PDF
- Proc. Amer. Math. Soc. 146 (2018), 161-173 Request permission
Abstract:
We study the $L^q$-dimensions of self-affine measures and the Käenmäki measure on a class of self-affine sets similar to the class considered by Hueter and Lalley. We give simple, checkable conditions under which the $L^q$- dimensions are equal to the value predicted by Falconer for a range of $q$. As a corollary this gives a wider class of self-affine sets for which the Hausdorff dimension can be explicitly calculated. Our proof combines the potential theoretic approach developed by Hunt and Kaloshin with recent advances in the dynamics of self-affine sets.References
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Additional Information
- Jonathan M. Fraser
- Affiliation: School of Mathematics, The University of St Andrews, St Andrews, KY16 9SS, United Kingdom
- MR Author ID: 946983
- Email: jmf32@st-andrews.ac.uk
- Tom Kempton
- Affiliation: School of Mathematics, The University of Manchester, Manchester, M13 9PL, United Kingdom
- Email: thomas.kempton@manchester.ac.uk
- Received by editor(s): July 8, 2016
- Received by editor(s) in revised form: January 19, 2017
- Published electronically: August 1, 2017
- Additional Notes: The authors were financially supported by an LMS Scheme 4 Research in Pairs grant. The second author also acknowledges financial support from the EPSRC grant EP/K029061/1, and the first author acknowledges financial support from a Leverhulme Trust Research Fellowship (RF-2016-500).
The authors thank the Universities of Manchester and St Andrews for hosting the research visits which led to this work and Kenneth Falconer and Antti Käenmäki for helpful discussions. - Communicated by: Nimish Shah
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 161-173
- MSC (2010): Primary 28A80, 28A78, 37C45
- DOI: https://doi.org/10.1090/proc/13672
- MathSciNet review: 3723130