On the L^q Dimensions of Measures on Hueter-Lalley Type Self-Affine Sets

Abstract

We study the L^q -dimensions of self-affine measures and the Kaenmaki 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 Lq -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.