A note on a smoothing property of the harmonic Bergman projection

Abstract

It is proved that on any smoothly bounded domain $D$ in ${\mathbb{R}}^n$, $n>1$, the output of the harmonic Bergman projection belongs to the Sobolev space of order $k$ whenever all tangential derivatives of order up to k of the input function belong to $L^2(D)$.

References in corpus (1)

• Duality of holomorphic functions spaces und smoothing properties of the Bergman projection