Uniformly perfect measures on strictly convex planar graphs are $L^{2}$-flattening
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911267447373824 |
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| author | Algom, Amir Orponen, Tuomas |
| author_facet | Algom, Amir Orponen, Tuomas |
| contents | Uniformly perfect measures are a common generalisation of Ahlfors regular measures, self-conformal measures on the line, and their push-forwards under sufficiently regular maps. We show that every uniformly perfect measure $σ$ on a strictly convex planar $C^{2}$-graph is $L^{2}$-flattening. That is, for every $ε>0$, there exists $p = p(ε,σ) \geq 1$ such that $$\|\hatσ\|_{L^{p}(B(R))}^{p} \lesssim_{ε,σ} R^ε, \qquad R \geq 1.$$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_09354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniformly perfect measures on strictly convex planar graphs are $L^{2}$-flattening Algom, Amir Orponen, Tuomas Classical Analysis and ODEs 28A80, 42B10 Uniformly perfect measures are a common generalisation of Ahlfors regular measures, self-conformal measures on the line, and their push-forwards under sufficiently regular maps. We show that every uniformly perfect measure $σ$ on a strictly convex planar $C^{2}$-graph is $L^{2}$-flattening. That is, for every $ε>0$, there exists $p = p(ε,σ) \geq 1$ such that $$\|\hatσ\|_{L^{p}(B(R))}^{p} \lesssim_{ε,σ} R^ε, \qquad R \geq 1.$$ |
| title | Uniformly perfect measures on strictly convex planar graphs are $L^{2}$-flattening |
| topic | Classical Analysis and ODEs 28A80, 42B10 |
| url | https://arxiv.org/abs/2509.09354 |