9 problems

Stein–Iosevich–Sawyer conjecture. If $0<q\leq \tfrac12$ and this estimate holds, then $\mathcal{M}$ is bounded on $L^p$ for every $p>1/q$.

Integer-power conjecture. The only dimension functions $\alpha$ for which there exists an $\alpha$-set $E$ supporting a measure $\mu$ satisfying this Fourier decay condition are in…

Let $s\in (0,1]$. The sharp decay exponent is the quantity $\min\\{1+s,3s\\}$. Orponen's conjecture. For every $s\in (0,1]$, the sharp decay should be $\min\\{1+s,3s\\}$. This conj…

Let $u$ be a self-conformal measure on $mathbb{C}$ that is not conjugate to a linear system and is supported on an analytic curve that is not a line. **Polynomial Fourier decay co…

Let $u$ be a compactly supported probability measure on $mathbb{R}^d$ satisfying … and … Assume that $\alpha>2d/3$. Three-term progression distance conjecture. Under appropriate q…

Let $\rho>0$ and let $\rho$-Fourier decay mean that a measure $u$ satisfies the decay inequality … Suppose $Gamma$ is a smooth hypersurface and a measure $mu$ defined on $Gamma$ s…

Let $k$ be the number of nonvanishing principal curvatures of the underlying compact smooth hypersurface, and consider the bilinear local maximal operator $\mathrm{M}_\sigma^{loc}$…

Let $m=2$, and let $\mathrm{M}_\sigma^{loc}$ and $\mathrm{M}_\sigma$ denote the multilinear local and global maximal functions associated with a measure whose Fourier transform sat…

Stein–Iosevich–Sawyer conjecture. Under this Fourier-decay assumption, $\mathcal M$ is bounded on $L^p(\mathbb R^n)$ for every $p>1/\beta$. The conjecture extends the previously kn…