3 problems

Sharp Sobolev regularity conjecture. The operator $\mathfrak R$ boundedly maps $L^p$ to $L_\alpha^p$ for $\alpha \le \alpha(p)$. The sharp $L^p$ regularity estimate is open in high…

Finite-type Sobolev improving conjecture. The operator $A_{\gamma}$ maps $L^p$ to $L^p_{\alpha}$ for all $p\geq 2$ and

Non-degenerate curve Sobolev improving conjecture. If $\gamma$ is non-degenerate and $2n-2<p<\infty$, then