6533b831fe1ef96bd1299916
RESEARCH PRODUCT
On arithmetic sums of Ahlfors-regular sets
Hannu Tuomas Orponensubject
sum-product problemkombinatoriikkaMathematics::General TopologyHausdorff dimensionMetric Geometry (math.MG)11B30 (primary) 28A80 (secondary)Mathematics - Metric GeometryMathematics - Classical Analysis and ODEsAhlfors-regular setsaritmetiikkaClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematics::Metric GeometryMathematics - CombinatoricsmittateoriaCombinatorics (math.CO)Geometry and TopologyAnalysisdescription
Let $A,B \subset \mathbb{R}$ be closed Ahlfors-regular sets with dimensions $\dim_{\mathrm{H}} A =: \alpha$ and $\dim_{\mathrm{H}} B =: \beta$. I prove that $$\dim_{\mathrm{H}} [A + \theta B] \geq \alpha + \beta \cdot \tfrac{1 - \alpha}{2 - \alpha}$$ for all $\theta \in \mathbb{R} \, \setminus \, E$, where $\dim_{\mathrm{H}} E = 0$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-04-15 | Geometric and Functional Analysis |