On embeddings, traces and multipliers in harmonic function spaces

Miloš Arsenović, Romi F. Shamoyan

This paper is devoted to certain applications of classical Whitney decomposition of the upper half space $\mathbb R^{n+1}_+$ to various problems in harmonic function spaces in the upper half space. We obtain sharp new assertions on embeddings, distances and traces for various spaces of harmonic functions. New sharp theorems on multipliers for harmonic function spaces in the unit ball are also presented.