The Journal of Geometric Analysis

, Volume 8, Issue 4, pp 629–653

A Hardy space for Fourier integral operators

  • Hart F. Smith

DOI: 10.1007/BF02921717

Cite this article as:
Smith, H.F. J Geom Anal (1998) 8: 629. doi:10.1007/BF02921717


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.

Math Subject Classifications

35S30 42B25 46E30 

Key Words and Phrases

Hardy space Littlewood-Paley theory Fourier integral operators 

Copyright information

© Mathematica Josephina, Inc. 1998

Authors and Affiliations

  • Hart F. Smith
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattle

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