On local oscillatory integrals with variable Calderon-Zygmund kernels, II

Let lambda epsilon R, Phi be a real analytic. function or a real-C-infinity function on R-n x R-n, phi epsilon C-0(infinity)(R-n x R-n) and k be a var iable Calderon-Zygmund kernel. Define the oscillatory singular integral ope rator T-lambda by T lambda f(x) = p. v. integral(En) e(i lambda Phi(x, y))k(x, x - y)phi(x, y )f(y) dy. When n = 1, the authors prove that T-lambda are bounded uniformly in lambda from the variant Hardy space H-E(1)(R) into L-1(R). Moreover for any n eps ilon N, when Phi(x, y) equivalent to Phi(x - y) and phi(x, y) equivalent to phi(x - y), the authors show that Tx are bounded on the weighted Hardy spa ce H-1(R-n, omega) uniformly in lambda for any omega epsilon A(1)(R-n).