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Endpoint Fourier restriction and unrectifiability
Published 15 Apr 2021 in math.CA | (2104.07482v1)
Abstract: We show that if a measure of dimension $s$ on $\mathbb{R}d$ admits $(p,q)$ Fourier restriction for some endpoint exponents allowed by its dimension, namely $q=\tfrac{s}{d}p'$ for some $p>1$, then it is either absolutely continuous or $1$-purely unrectifiable.
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