A generalized Fatou theorem

Mair, B. A.; Singman, David

doi:10.1090/S0002-9947-1987-0876474-7

A generalized Fatou theorem
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by B. A. Mair and David Singman

Trans. Amer. Math. Soc. 300 (1987), 705-719

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

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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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