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

Authors: ALEM MEMIC

Abstract: In this paper for 1\leq p<\infty we introduce a space A^p(\Omega\backslash K) of all functions u\in b^p(\Omega\backslash K) such that there exist v\in b^p(\Omega) and w\in b^p(R^n\backslash K) such that u=v+w on \Omega\backslash K, and we give a characterization of it. For the case p=2 we get a reproducing kernel for a Hilbert space A^2(\Omega\backslash K), after which we obtain a characterization and its useful properties.

Keywords: Bergman spaces, harmonic function, reproducing kernel, removable singularity

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