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)

PDF- CLASSICAL ANALYSIS AND ODES

- ANALYSIS OF PDES

- COMBINATORICS

- METRIC GEOMETRY