Endpoint estimates for a class of multilinear oscillatory singular integral operators

Some endpoint estimates for a class of multilinear oscillatory singular integral operators are considered and their boundedness from Hardy space H-1 (R-n) to Lebesgue space L-1 (R-n) and from Her z-type Hardy space H (K) over circle (n(1 - 1/q))(q), (p) (R-n) (or HKqn(1 - 1/q), (p) (R-n)) to Herz space (K) over circle (n(1 - 1/q), p)(q) (R-n) (or K-q(n(1 - 1/q), p) (R-n)) are obtained for any p is an element of (0, infinity) and q is an element of (1, infinity).