We introduce new function spaces $\mathcal{ L}_{ W,s}^{ q,p}(\mathbb{ R}^{ n})$ that yield a natural reformulation of the $\ell^{ q}L^{ p}$ 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 $p=q$, 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.
Categories: math.AP math.CA
