On multilinear oscillatory integrals, nonsingular and singular
arXiv:math/0311039
Abstract
Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. Lebesgue space norm inequalities are established for multilinear integral operators of Calderon-Zygmund type which incorporate oscillatory factors exp(iP), where P is a real-valued polynomial with large coefficients. A related problem concerning upper bounds for measures of sublevel sets is solved.
24 pages. See also http://www.math.berkeley.edu/~mchrist/preprints.html