A note on a smoothing property of the harmonic Bergman projection
  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 $L^2(D)$. 
A.-K. Herbig
math.CV