English

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.

Keywords

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

R2 v1 2026-06-22T22:38:22.627Z