Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases
Classical Analysis and ODEs
2019-05-21 v1
Abstract
We obtain sharp bounds for oscillatory integral operators with generic homogeneous polynomial phases in several variables. The phases considered in this paper satisfy the rank one condition which is an important notion introduced by Greenleaf, Pramanik and Tang. Under certain additional assumptions, we can establish sharp damping estimates with critical exponents to prove endpoint estimates.
Cite
@article{arxiv.1905.07980,
title = {Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases},
author = {Danqing He and Zuoshunhua Shi},
journal= {arXiv preprint arXiv:1905.07980},
year = {2019}
}
Comments
14 pages