Resumen de Semi-global solutions of [... ] with L(p)(1 < or = p < or = infinity) bounds on strongly pseudoconvex real hypersurfaces in C(n)(n > or = 3)

H.P. Lee, C. H. Chang

• Let $M$ be an open subset of a compact strongly pseudoconvex hypersurface $\{\rho = 0\}$ defined by $M = D \times {\mathbf C}^{n-m}\cap \{\rho = 0\}$, where $1 \le m \le n-2$, $D = \{\sigma(z_1,\ldots, z_m) < 0\} \subset {\mathbf C}^m$ is strongly pseudoconvex in ${\mathbf C}^m$. For $\bar\partial_b$ closed $(0,q)$ forms $f$ on $M$, we prove the semi-global existence theorem for $\bar {\partial}_b$ if $1 \le q \le n-m-2$, or if $q=n-m-1$ and $f$ satisfies an additional "moment condition". Most importantly, the solution operator satisfies $L^p$ estimates for $1\le p\le \infty$ with $p=1$ and $\infty$ included.