Boundary Values of Harmonic Bloch Functions in Lipschitz Domains: A Martingale Approach

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Abstract

In this paper, the boundary behaviour of a certain class of harmonic functions in Lipschitz domains is studied. It continues the work of N. Makarov on the boudary behaviour of analytic Bloch functions in the unit disk. Certain means associated with the function allow to approximate it by a martingale, and the boudary properties of the function are transferred to the asymptotic behaviour of the martingale.

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