A homotopy formula for $a_q$ domains in complex manifolds

Abstract

We construct a global homotopy formula for $a_q$ domains in a complex manifold. The homotopy operators in the formula will gain $1/2$ derivative in Hölder-Zygmund spaces ${\Lambda }^r$ when the boundaries of the domains are in ${\Lambda }^{r+3}$ with $r>0$.

arXiv comment24 pages. Improved the main results