ABSTRACT
Theorem 19.4. Suppose that the integrol operotor defined by the kernel function k is regular from X =Lp([-l,l]) into Y = L r ([-l, 1]), where p < r < 00. Assume that the estimates (9.36) hold, where the functions a, b, c, and d are defined by
aCt, T,S, 0') = te-(t-''')/·k(05,O'), b(t,T,,,,O') = te-(t-"')/-k(",-u),
c(t, T, ", 0') = - ~e(t-"')/-k(-"'0'), d(t, T, '" 0') = - ~e(t-.,.)/-k(-I, -0').
