We prove some theorems on uniqueness of meromorphic mappings into complex projective space ℙⁿ(ℂ), which share 2n+3 or 2n+2 hyperplanes with truncated multiplicities.

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 $ϵ\>0$,...

We show that for an interpolating sequence in the polydisk one can construct a universal divisor for Hardy spaces.

We study a division problem in the Hardy classes $H^p\left(\right)$ of the unit ball of ${ℂ}^2$ which generalizes the $H^p$ corona problem, the generators being allowed to have common zeros. MPrecisely, if S is a subset of , we study conditions on a ${ℂ}^k$-valued bounded Mholomorphic function B, with $B_{|S}=0$, in order that for 1 ≤ p < ∞ and any function $f\in H^p\left(\right)$ with $f_{|S}=0$ there is a ${ℂ}^k$-valued $H^p\left(\right)$ holomorphic function F with f = B·F, i.e. the module generated by the components of B in the Hardy class $H^p\left(\right)$ is the entire module $M_S:=f\in H^p\left(\right):f_{|S}=0$. As a special case,...