2023
DOI: 10.1112/jlms.12767
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The Lq$L^q$ spectrum of self‐affine measures on sponges

Abstract: In this paper, a sponge in double-struckRd$\mathbb {R}^d$ is the attractor of an iterated function system consisting of finitely many strictly contracting affine maps whose linear part is a diagonal matrix. A suitable separation condition is introduced under which a variational formula is proved for the Lq$L^q$ spectrum of any self‐affine measure defined on a sponge for all q∈double-struckR$q\in \mathbb {R}$. Apart from some special cases, even the existence of their box dimension was not proved before. Under … Show more

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