On multilinear oscillatory integrals, nonsingular and singular
Michael Christ, Xiaochun Li, Terence Tao, Christoph Thiele
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.
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