A reproducing kernel for a Hilbert space related to harmonic Bergman space on a domain outside compact set

In this paper for 1 ≤ p ∞ we introduce a space A^p (ΩK) of all functions u ∈ b^p (ΩK) such that there exist v ∈ b^p (Ω) and w ∈ b^p (R^nK) such that u = v + w on ΩK , and we give a characterization of it. For the case 2 p = 2 we get a reproducing kernel for a Hilbert space A^2 (ΩK), after which we obtain a characterization and its useful properties.