BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev spaces.
The spectral synthesis theorem for Sobolev spaces of Hedberg and Wolff [7] has been applied in combination with duality, to problems of L approximation by analytic and harmonic functions. In fact, such applications were one of the main motivations to consider spectral synthesis problems in the Sobolev space setting. In this paper we go the opposite way in the context of the BMO-H duality: we prove a BMO approximation theorem by harmonic functions and then we apply the ideas in its proof to produce...