Trace theorems in harmonic function spaces on $(\mathbb R^{n+1}_+)^m$, multipliers theorems and related problems

Miloš Arsenović, Romi F. Shamoyan

We introduce and study properties of certain new harmonic function spaces in products of upper half spaces. Norm estimates for the so called expanded Bergman projection are obtained. Sharp theorems on multipliers acting on certain Sobolev type spaces of harmonic functions on the unit ball are obtained.