< (,

The hypotheses of Theorem 13.10 and, in particular, the Lt-continuity of the kernels I, m and n hold if I, m and n are jointly continuous. However, as was shown in FROLOVA-KALITVIN-ZABREJKO [1997) and KALITVIN-FROLOVA [1995), the kernel functions I, m and n are still Lt-continuous if they are discontinuous only along finitely many surfaces with continuous parameter representations T = T(<p, t, s) and 0' =O'(<p,t,s). We point out that many partial integral equations which arise in applications have to be considered, for physical reasons, neither in ideal spaces nor in spaces of continuous functions. Therefore, partial integral equations in other spaces are of particular interest, as those studied in KALITVIN-JANKELEVICH [1994), KALITVIN-DEMANOVA [1995), KALITVIN-KoLESNIKOVA [1995), or KALITVIN-NASONOV [1996}.