A stationary set method for estimating oscillatory integrals
Classical Analysis and ODEs
2021-10-13 v3 Algebraic Geometry
Logic
Number Theory
Abstract
We propose a new method of estimating oscillatory integrals, which we call a stationary set method. We use it to obtain the sharp convergence exponents of Tarry's problems in dimension two for every degree . As a consequence, we obtain sharp Fourier extension estimates for a family of monomial surfaces.
Cite
@article{arxiv.2103.08844,
title = {A stationary set method for estimating oscillatory integrals},
author = {Saugata Basu and Shaoming Guo and Ruixiang Zhang and Pavel Zorin-Kranich},
journal= {arXiv preprint arXiv:2103.08844},
year = {2021}
}
Comments
Added an argument showing sharpness of the main result in an average sense; shared to us by Wright