2000 character limit reached
Duality of holomorphic functions spaces und smoothing properties of the Bergman projection (1110.1533v1)
Published 7 Oct 2011 in math.CV
Abstract: Let $\Omega\subset\mathbb{C}n$ be a bounded domain with smooth boundary, whose Bergman projection $B$ maps the Sobolev space $H{k_{1}}(\Omega)$ (continuously) into $H{k_{2}}(\Omega)$. We establish two smoothing results: (i) the full Sobolev norm $|Bf|{k{2}}$ is controlled by $L2$ derivatives of $f$ taken along a single, distinguished direction (of order $\leq k_{1}$), and (ii) the projection of a conjugate holomorphic function in $L{2}(\Omega)$ is automatically in $H{k_{2}}(\Omega)$. There are obvious corollaries for when $B$ is globally regular.