7 problems

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…

Linear smoothing conjecture for FIOs. For any $p\geq\overline{p}_d$ and $\sigma<\frac{1}{p}$, one has

Boutet de Monvel's conjecture. There is a maximal $\epsilon_0>0$ such that, for every $\epsilon\in(0,\epsilon_0)$, the extended flows define a real-analytic diffeomorphism

Higher-order Compton scattering smoothing conjecture. For each scattering order $i$, $g_i$ is approximated by a Fourier integral operator $\mathcal{L}_i(\cdot,n_e)$ of order

Higher-dimensional logarithmic-phase FUP conjecture. For each $\nu>0$ there exists $\beta=\beta(\nu)>0$ such that

Signature-refined local smoothing conjecture. There is $1/p-$ local smoothing for $\mathcal{F}$, meaning that the local smoothing estimate holds for every $\sigma<1/p$, for all…

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 $t$,