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Tangential boundary behavior of functions in Dirichlet-type spaces. (English) Zbl 0531.31007
Let h be an harmonic function on the unit disc U. It is well known that the limits of h along curves which approach the boundary tangentially may not exist. In this work, regions making exponential contact or polynomial contact are defined, and it is proved that for some subspaces of the harmonic functions analogous to the classical Dirichlet spaces, it is possible to obtain maximal inequalities of Hardy-Littlewood type. This leads to theorems of Fatou for tangential limits of some classes of functions, for example Cauchy integrals of functions of bounded variation on the boundary.
Reviewer: J.Lacroix

MSC:
31B25 Boundary behavior of harmonic functions in higher dimensions
31C25 Dirichlet forms
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