Abstract :
In this paper, for the multilinear oscillatory singular integral operators TA defined by
TAf (x) = p.v. Rn
eiP (x,y) Ω(x − y)
|x −y|n+m
Rm+1(A;x, y)f (y)dy, n 2,
where P(x, y) is a nontrivial and real-valued polynomial defined on Rn×Rn, Ω(x) is homogeneous
of degree zero on Rn, A(x) has derivatives of order m in Λ˙β (0 < β <1), Rm+1(A;x, y) denotes
the (m + 1)th remainder of the Taylor series of A at x expended about y, the author proves that
if Ω ∈ Lq(Sn−1) for some q > 1/(1 −β), then for any p ∈ (1,∞), TA is bounded on Lp(Rn).
Meanwhile, the weighted Lp-boundedness of TA is also given.
2004 Elsevier Inc. All rights reserved.
