8 problems

Let $U_{1},U_{2},U_{3}\subset U$ be a $\nu$-disjoint triple of squares, meaning that each has side length comparable to $\nu$ and distinct squares are separated by at least $\nu$.…

Let $k\geq 2$. Let $S_1,\ldots,S_k\subseteq\mathbb{R}^{d}$ be smooth hypersurfaces equipped with measures $\sigma_1,\ldots,\sigma_k$, respectively. They are transversal if there is…

Let $0<\delta\leq\nu<1$. Three families $\mathbb{T}_{1},\mathbb{T}_{2},\mathbb{T}_{3}$ of $\delta$-tubes are $\nu$-disjoint when their orientations lie in spherical patches of diam…

Let $T$ be a multilinear Calderón–Zygmund operator, let $p_1,\ldots,p_m\in(1,\infty)$, and define $p$ by $1/p=1/p_1+\cdots+1/p_m$. For weights…

Let $\tau_1,\tau_2,\tau_3\subset[-1,1]^3$ be cubes of side length comparable to $1$ satisfying … where $n(\xi)=(-2\xi_1,-2\xi_2,-2\xi_3,1)$ is the normal vector to the paraboloid.…

Let $S_1,\ldots,S_{n+1}\subset\mathbb{R}^{n+1}$ be hypersurfaces, and let $d\sigma_i$ denote the surface measure on $S_i$. For functions $f_i$ on $S_i$, consider the multilinear re…

Let $S_1,\ldots,S_d$ be transversal smooth codimension-one submanifolds of $\mathbb{R}^d$, with induced measures $d\sigma_j$. Let $p'$ be the Hölder conjugate of $p$. Strengthened…

Let $2\leq k\leq d$. A $k$-tuple $S_1,\ldots,S_k$ of smooth codimension-one submanifolds of $\mathbb{R}^d$ is transversal if the wedge product of any choice of unit normal vectors…