# Sparse bounds for pseudodifferential operators

@article{Beltran2017SparseBF,
title={Sparse bounds for pseudodifferential operators},
journal={Journal d'Analyse Math{\'e}matique},
year={2017},
volume={140},
pages={89-116}
}
• Published 7 November 2017
• Mathematics
• Journal d'Analyse Mathématique
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.
14 Citations
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