Local smoothing and Hardy spaces for Fourier integral operators

We show that the Hardy spaces for Fourier integral operators form natural spaces of initial data when applying $p-decoupling inequalities to local smoothing for the wave equation. This yields new local smoothing estimates which, in a quantified manner, improve the bounds in the local smoothing conjecture on Rn for p >= 2(n + 1)/(n - 1), and complement them for 2 < p < 2(n + 1)/(n - 1). These estimates are invariant under application of Fourier integral operators, and they are essentially sharp.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).