The harmonic Bergman kernel and the Friedrichs operator
The harmonic Bergman kernel Q(Omega) for a simply connected planar domain Q can be expanded in terms of powers of the Friedrichs operator F-Omega if parallel toF(Omega)parallel to <1 in operator norm. Suppose that &UOmega; is the image of a univalent analytic function φ in the unit disk with φ '(z)=1+ψ(z) where ψ(0)=0. We show that if the function ψ belongs to a space D-s(D), s>0, of Dirichlet
