HARDY-SPACES AND OSCILLATORY SINGULAR-INTEGRALS .2.

We consider oscillatory singular integral operators with real-analytic phases. The uniform boundedness from H-E(1) --> L(1) of such operators is proved, where H-E(1) is a variant of the standard Hardy space H-1. The result is false for general C-infinity phases. This work is a continuation of earlier work by Phong and Stein (on bilinear phases) and the author (on polynomial phases).