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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Generalized local Fatou theorems and area integrals

Authors: B. A. Mair, Stan Philipp and David Singman
Journal: Trans. Amer. Math. Soc. 321 (1990), 401-413
MSC: Primary 31B25
MathSciNet review: 974520
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Abstract: Let $ X$ be a space of homogeneous type and $ W$ a subset of $ X \times (0,\infty )$. Then, under minimal conditions on $ W$, we obtain a relationship between two modes of convergence at the boundary $ X$ for functions defined on $ W$. This result gives new local Fatou theorems of the Carleson-type for solutions of Laplace, parabolic and Laplace-Beltrami equations as immediate consequences of the classical results. Lusin area integral characterizations for the existence of limits within these more general approach regions are also obtained.

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Article copyright: © Copyright 1990 American Mathematical Society