On Weights Which Admit Harmonic Bergman Kernel and Minimal Solutions of Laplace’s Equation

Abstract In this paper we consider spaces of weight square-integrable and harmonic functions L 2 H (Ω, µ ). Weights for which there exists reproducing kernel ) are named ’admissible weights’ such kernels ’harmonic Bergman kernels’. We prove that if only integration is integrable in some negative power, then it admissible. Next construct a on the unit circle non-admissible using Bell-Ligocka theorem show weights exist large class domains ℝ . Later conclude from classical result Hilbert theory set { f ∈ |f ( z = c } admissible non-empty, exactly one element with minimal norm. Such an called ’a z, )-solution Laplace’s equation Ω’ upper estimates given.