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 Laplaceâs 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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