On holomorphic extension of hyperfunctions

Let $D$ be a bounded domain in $\mathbb{C}^m$, $m>1$, with connected real-analytic boundary and let $U(\zeta,z)$ be the kernel of the Bochner-Martinelli integral representation.
Theorem. If $T$ is a hyperfunction on $\partial D$ and$M^kT$ is the iteration of boundary values of the Bochner-Marlinelli transform from the inside of the domain, then the sequence of $M^kT$ converges weakly to some $CR$-hyperfunction $S$ given on $\partial D$.
The Bochner–Martinelli transform presents a harmonic function beyond $\partial D$ which equals $T_\zeta(U(\zeta,z))$.
This assertion generalizes some results by Polking and Walk, Romanov, and one of the authors.