Sparse bounds for pseudodifferential operators

  title={Sparse bounds for pseudodifferential operators},
  author={David Beltran and Laura Cladek},
  journal={Journal d'Analyse Math{\'e}matique},
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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