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On the $ L^q$-dimensions of measures on Hueter-Lalley type self-affine sets


Authors: Jonathan M. Fraser and Tom Kempton
Journal: Proc. Amer. Math. Soc. 146 (2018), 161-173
MSC (2010): Primary 28A80, 28A78, 37C45
DOI: https://doi.org/10.1090/proc/13672
Published electronically: August 1, 2017
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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.


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Additional Information

Jonathan M. Fraser
Affiliation: School of Mathematics, The University of St Andrews, St Andrews, KY16 9SS, United Kingdom
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

DOI: https://doi.org/10.1090/proc/13672
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
Article copyright: © Copyright 2017 American Mathematical Society

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