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Boundary values of harmonic Bloch functions in Lipschitz domains: A martingale approach. (English) Zbl 0924.31004
The author extends some results on the boundary behaviour of analytic Bloch functions in the unit disk, to the case of Lipschitz domains in higher dimensions. The principal tool is to assign to any harmonic Bloch function in a Lipschitz domain a dyadic martingale with respect to harmonic measure. Some of the classical results, extended to this case, are direct consequences of their martingale counterparts.
Reviewer: L.Popa (Iaşi)

MSC:
31B25 Boundary behavior of harmonic functions in higher dimensions
60G42 Martingales with discrete parameter
30D45 Normal functions of one complex variable, normal families
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