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This paper is devoted to certain applications of classical Whitneydecomposition of the upper half space R^n+1 to various problems in harmonicfunction spaces in the upper half space.We obtain sharp new assertions onembeddings,distances and traces for various spaces of harmonic functions Newsharp theorems on multipliers for harmonic function spaces in the unit ball arealso presented .

On Embeddings,Traces and Multipliers in harmonic function spaces