NONCONVOLUTION OPERATORS WITH OSCILLATING-KERNELS THAT MAP B-1(0,1) INTO ITSELF AND MAP L(P) INTO

Here we consider the kernels Omega(1)(y, u) = K(y, u)e(i\y-u\a) for a > I. We show that the operators Tf(y) = integral (Omega(1)(y + 1/2, u) - Omega(1)(y, u))f(u) du map B(R(n)) into itself. We also show that the operators integral (Omega(1)(y, u)) f(u) du map L(p) into itself for p > 1. (C) 1995 Academic Press, Inc.