3 problems

Local $L_1$ wave propagator conjecture. If $\alpha>1/2$, then there exists a constant $C_{\alpha,c}$ such that, for all $\epsilon\leq1/4$ and sufficiently small $t$,

Higher-dimensional Grushin wave-estimate conjecture. For every ${\mathscr{C}}_1>0$, $t>0$, $1\leq p\leq\infty$, and $\alpha>(d-1)|1/p-1/2|$, there exists a constant…

Mikhlin–Hörmander multiplier conjecture. The operator $m(G)$ is bounded on $L_p$ for $1<p<\infty$ and is of weak type $(1,1)$ whenever $s>1$.