4 problems

Chen–Véron conjecture. In dimensions $1$ and $2$, such a fundamental solution exists, is radial and locally integrable, and satisfies the displayed bound.

Estimate conjecture. The estimates hold whenever $N\geq3$.

Extension conjecture. The above result remains valid when $N\geq3$, up to some modifications of the estimates.

Fundamental-solution conjecture. The fundamental solution $\Phi_{\ln}$ exists for $N=1,2$ and satisfies