Characterizations of Hardy spaces for Fourier integral operators

Abstract

We prove several characterizations of the Hardy spaces for Fourier integral operators Hp FIO(Rn), for 1 < p < 1. First we characterize Hp FIO(Rn) in terms of Lp(Rn)-norms of parabolic frequency localizations. As a corollary, any characterization of Lp(Rn) yields a corresponding version for Hp FIO(Rn). In particular, we obtain a maximal function characterization and a characterization in terms of vertical square functions. Show more