Sparse bounds for pseudodifferential operators
Classical Analysis and ODEs
2018-03-23 v2
Abstract
We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of weighted estimates for pseudodifferential operators. The results naturally apply to the context of oscillatory Fourier multipliers, with applications to dispersive equations and oscillatory convolution kernels.
Cite
@article{arxiv.1711.02339,
title = {Sparse bounds for pseudodifferential operators},
author = {David Beltran and Laura Cladek},
journal= {arXiv preprint arXiv:1711.02339},
year = {2018}
}
Comments
21 pages, 2 figures. Revised version. To appear in J. Anal. Math