Let K be a kernel on Rn, that is, K is a non-negative, unbounded L1 function that is radially symmetric and decreasing. We define the convolution K [midast ] F by

and note from Lp-capacity theory [11, Theorem 3] that, if F ∈ Lp, p > 1, then K [midast ] F exists as a finite Lebesgue integral outside a set A ⊂ Rn with CK,p(A) = 0. For a Borel set A,

where

We define the Poisson kernel for Rn+1+ = {(x, y) [ratio ] x ∈ Rn, y > 0} by

and set

Thus u is the Poisson integral of the potential f = K [midast ] F, and we write

We are concerned here with the limiting behaviour of such harmonic functions at boundary points of Rn+1+, and in particular with the tangential boundary behaviour of these functions, outside exceptional sets of capacity zero or Hausdorff content zero.