Function spaces for decoupling
Andrew Hassell, Pierre Portal, Jan Rozendaal, Po‐Lam Yung
Source abstract
Abstract 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.
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