On a New Type of Spaces Related to the Decomposition Theorem for Harmonic Functions

If 1 ≤ p ∞, Ω an open subset of R^n and K a compact subset of , we consider the space A^p ( Ω\K) of all functions u ∈ b^p ( Ω\K) that can be decomposed as u = v+w on Ω\K, where v ∈ b^p (Ω ) and w ∈ b^p (R^n\K). In this paper we introduce an analogous de nitions for networks and for holomorphic functions. In nal, we develop a new type of regularity for distributions and obtain their useful properties.