7 problems

Let $0<\delta<1$ and $\kappa\in\mathbb{N}$ with $\kappa>\frac{20}{\delta}$. For $1<q<\infty$, $0<\varepsilon,\nu<1$, let…

Let $R$ be a large parameter, let $B_R$ be a ball or cube of radius or side length $R$ in ${\mathbb R}^3$, and let $E_SF$ be the extension operator for the two-dimensional parabolo…

Let $R$ be a large parameter, let $B_R$ be a ball or cube of radius or side length $R$ in ${\mathbb R}^3$, and let $E_SF$ denote the Fourier extension operator associated to the tw…

Restriction conjecture. The estimate

Let $k\geq2$, and let $U_1,\ldots,U_k$ parametrize transversal caps of the paraboloid $x\mapsto|x|^2$ in $\mathbb{R}^{d+1}$. For functions $g_j$ on $U_j$, write $p'$ for the Hölder…

Let $n\geq 2$, let $N$ be an odd positive integer, and let $\mathcal{E}$ denote the extension operator for the paraboloid over $\mathbb Z/N\mathbb Z$, acting on functions $H$ on…

Let $S$ be a non-empty smooth compact subset of the paraboloid … where $n\geq1$, and let $\mathrm{d}\sigma$ be the pull-back of $n$-dimensional Lebesgue measure under the projectio…