An $L^2$-identity and pinned distance problem

23 Jun 2018 Liu Bochen

Let $\mu$ be a Frostman measure on $E\subset\mathbb{R}^d$. The spherical average decay $$\int_{S^{d-1}}|\widehat{\mu}(r\omega)|^2\,d\omega\lesssim r^{-\beta} $$ was originally used to attack Falconer distance conjecture, via Mattila's integral... (read more)

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