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arXiv · 2104.07514

On arithmetic sums of Ahlfors-regular sets

Tuomas Orponen
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Abstract

Let $A,B \subset \mathbb{R}$ be closed Ahlfors-regular sets with dimensions $\dim_{\mathrm{H}} A =: α$ and $\dim_{\mathrm{H}} B =: β$. I prove that $$\dim_{\mathrm{H}} [A + θB] \geq α+ β\cdot \tfrac{1 - α}{2 - α}$$ for all $θ\in \mathbb{R} \, \setminus \, E$, where $\dim_{\mathrm{H}} E = 0$.

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Tuomas Orponen. 2021-11-28. On arithmetic sums of Ahlfors-regular sets. https://arxiv.org/abs/2104.07514

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