A Hardy space for Fourier integral operators
- Cite this article as:
- Smith, H.F. J Geom Anal (1998) 8: 629. doi:10.1007/BF02921717
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We introduce a new function space, denoted by HFIO1(ℝn), which is preserved by the algebra of Fourier integral operators of order 0 associated to canonical transformations. A subspace of L1 (ℝn), this space in many aspects resembles the real Hardy space of Fefferman-Stein. In particular, we obtain an atomic characterization of HFIO1 (ℝn). In contrast to the standard Hardy space, these atoms are localized in frequency space as well as in real space.