In this Note, I prove that, in many cases, the injective Kobayashi pseudodistance, as defined by Hahn, is equal to the Kobayashi pseudodistance.

We study the $\bar{\partial }$-equation with Hölder estimates in $q$-convex wedges of ${ℂ}^n$ by means of integral formulas. If $D\subset {ℂ}^n$ is defined by some inequalities $\{{\rho }_i\le 0\}$, where the real hypersurfaces $\{{\rho }_i=0\}$ are transversal and any nonzero linear combination with nonnegative coefficients of the Levi form of the ${\rho }_i$’s have at least $(q+1)$ positive eigenvalues, we solve the equation $\bar{\partial }f=g$ for each continuous $(n,r)$-closed form $g$ in $D$, $n-q\le r\le n$, with the following estimates: if $d$ denotes the distance to the boundary of $D$ and if $d^{\beta }g$ is bounded, then for all $ϵ\>0$,...