Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations
We consider second kind integral equations of the form x(s) - ʃΩ k(s, t)x(t) dt = y(s) (abbreviated x - Kx = y), in which Ω is some unbounded subset of Rn Let Xp denote the weighted space of functions x continuous on Ω and satisfying x(s) = O(|s| -p), s → ∞. We show that if the kernel k(s, t) decays like | s - t | -q as | s - t | → ∞ for some sufficiently large q (and some other mild conditions on
