Sparse bounds for pseudodifferential operators

Abstract

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.

arXiv comment21 pages, 2 figures. Revised version. To appear in J. Anal. Math