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A Hardy space for Fourier integral operators

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ABSTRACT

We introduce a new function space, denoted by H 1FIO (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 H 1FIO (ℝn). In contrast to the standard Hardy space, these atoms are localized in frequency space as well as in real space.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, 98195, Seattle, WA

    Hart F. Smith

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  1. Hart F. Smith
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Smith, H.F. A Hardy space for Fourier integral operators. J Geom Anal 8, 629–653 (1998). https://doi.org/10.1007/BF02921717

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  • DOI: https://doi.org/10.1007/BF02921717

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