The integral equation of the title is
It was studied in , though h(x) was written as x-1g(x-1) there, and using a method involving orthogonal Watson transformations, it was shown there that if h ∈ L2(0, ∞), then the equation has a solution f ∈ L2(0, ∞), and that / is given by
In this paper, using the techniques of , we shall show that the equation can be solved for ℎ in the space ℒμ, p of  for 1 ≤ p < ∘, μ > 0, and that for these spaces, which include L2(0, ∘), f is given by the simpler formula
We shall further show that these results can be extended to the spaces ℒw, μ, p of . This forms the content of our theorem below.