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

DOI:
https://doi.org/10.1090/S0002-9947-1987-0876474-7

MathSciNet review:
876474

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, a general Fatou theorem is obtained for functions which are integrals of kernels against measures on . 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1987-0876474-7

Keywords:
Fatou theorem,
Laplace equation,
maximal function,
weak type,
pseudo-distance,
parabolic equation,
-admissible,
-Lebesgue set

Article copyright:
© Copyright 1987
American Mathematical Society