A note on a smoothing property of the harmonic Bergman projection

TL;DR

This paper proves that the harmonic Bergman projection enhances regularity, mapping functions with tangential derivatives in L^2 to Sobolev spaces of corresponding order on smoothly bounded domains.

Contribution

It establishes a smoothing property of the harmonic Bergman projection relating tangential derivatives to Sobolev regularity.

Findings

Harmonic Bergman projection improves regularity based on tangential derivatives.

Output belongs to Sobolev space of order k under specified conditions.

Results apply to smoothly bounded domains in  > 1.

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 $L^2(D)$.