Transactions of the American Mathematical Society

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



A generalized Fatou theorem

Authors: B. A. Mair and David Singman
Journal: Trans. Amer. Math. Soc. 300 (1987), 705-719
MSC: Primary 31B25; Secondary 31C99, 42B25
MathSciNet review: 876474
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Abstract: In this paper, a general Fatou theorem is obtained for functions which are integrals of kernels against measures on $ {{\mathbf{R}}^n}$. These include solutions of Laplace's equation on an upper half-space, parabolic equations on an infinite slab and the heat equation on a right half-space. Lebesgue almost everywhere boundary limits are obtained within regions which contain sequences approaching the boundary with any prescribed degree of tangency.

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Keywords: Fatou theorem, Laplace equation, maximal function, weak type, pseudo-distance, parabolic equation, $ \alpha $-admissible, $ \Omega $-Lebesgue set
Article copyright: © Copyright 1987 American Mathematical Society