On multilinear oscillatory integrals, nonsingular and singular

TL;DR

This paper investigates multilinear oscillatory integrals, establishing Lebesgue space bounds for Calderon-Zygmund type operators with oscillatory factors and solving related measure estimation problems.

Contribution

It provides new Lebesgue space inequalities for multilinear oscillatory operators and addresses measure bounds for sublevel sets, extending classical analysis results.

Findings

Lebesgue space norm inequalities for multilinear oscillatory operators

Upper bounds for measures of sublevel sets

Extension of Calderon-Zygmund theory to oscillatory contexts

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.