9 problems

Uniform boundedness conjecture. For every $\epsilon>0$, uniformly over all collections ${\mathcal S}$ of disjoint strips,

Let $d\geq2$. Let $T_a^{\phi_1,\phi_2}$ be a bilinear Fourier integral operator whose non-degenerate phase functions satisfy the cinematic curvature condition, and let…

Let $T$ be the triangle operator considered in the paper, acting on pairs of functions on $\mathbb{R}^{d}$, and let $L^{p}\times L^{q}$ denote the corresponding product of Lebesgue…

Let $\operatorname{BMO}(\mathbb{R}^n)$ be the space of functions of bounded mean oscillation, and let $\operatorname{VMO}(\mathbb{R}^n)$ be Sarason's space of functions of vanishin…

Maximal-operator conjecture. The operator $B_{P,Q}^*$ is bounded from $l^2\times l^2$ into $l^{1,\infty}$. This is a maximal analogue of the boundedness questions for discrete bili…

Uniform coefficient conjecture. The constant $C_{P,Q}$ in the estimate

Bilinear fractional weight conjecture. The condition $\vec{w}\in A_{\vec{p},q}$ should imply

Let $T_\Omega$ be the bilinear rough operator in Theorem, and let $p,q,r$ satisfy $1/r=1/p+1/q$. Theorem proves the corresponding weighted estimate in its stated range, while Corol…

Calderón's conjecture. The bilinear Hilbert transform is bounded from $L^2\times L^2$ to $L^1$, that is, there exists a constant $C$ such that