4 problems

The non-resonant boundedness conjecture. Up to end-points, both operators have the boundedness range

Unified weighted-condition conjecture. There is a constant $C$ such that

Multilinear Marcinkiewicz integral extrapolation conjecture. If $\mu$ is bounded from $L^{q_1}({\mathbb R}^n)\times\cdots\times L^{q_m}({\mathbb R}^n)$ to $L^q({\mathbb R}^n)$ for…

Multilinear Hilbert transform boundedness conjecture. For $k\geq 1$ and exponents $1<p_1,\dots,p_k,p<\infty$ satisfying $\frac{1}{p}=\frac{1}{p_1}+\dots+\frac{1}{p_k}$, the truncat…