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Fourier Restriction Beyond Dimension Data: A Multiscale Moment Criterion
We establish an exact Fourier restriction criterion for a class of weighted Moran measures. Assuming uniformly bounded one-level frame bounds, we prove that, for every \(s>2\), the measure itself already detects the full extension estimate: \(L^2(μ)\to L^s(\mathbb R)\) extension holds if and only if
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