Sparse bounds for pseudodifferential operators

@article{Beltran2017SparseBF,
  title={Sparse bounds for pseudodifferential operators},
  author={David Beltran and Laura Cladek},
  journal={Journal d'Analyse Math{\'e}matique},
  year={2017},
  volume={140},
  pages={89-116}
}
We prove sparse bounds for pseudodifferential operators associated to Hörmander 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. 
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