Function spaces for decoupling

We introduce new function spaces that yield a natural reformulation of the decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half‐wave propagators, but not under all Fourier integral operators unless , in which case they coincide with the Hardy spaces for Fourier integral operators. We use these spaces to obtain improvements of the classical fractional integration theorem and local smoothing estimates.