Journal of Fourier Analysis and Applications

, Volume 6, Issue 5, pp 537–550 | Cite as

The characterization of the Triebel-Lizorkin spaces forp=∞

  • Huy-Qui Bui
  • Mitchell H. Taibleson


We establish the characterization of the weighted Triebel-Lizorkin spaces for p=∞ by means of a “generalized” Littlewood-Paley function which is based on a kernel satisfying “minimal” moment and Tauberian conditions. This characterization completes earlier work by Bui et al. The definitions of the Ḟ ∞,q α spaces are extended in a natural way to Ḟ ∞,∞ α and it is proven that this is the same space as Ḃ ∞,∞ α , which justifies the standard convention in which the two spaces are defined to be equal. As a consequence, we obtain a new characterization of the Hölder-Zygmund space Ḃ ∞,∞ α .

Math Subject Classifications

Primary 42B25 secondary 46E35 

Keywords and Phrases

Littlewood-Paley functions BMO, A weights Besov-Lipschitz spaces Triebel-Lizorkin spaces 


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Copyright information

© Birkhäuser Boston 2000

Authors and Affiliations

  • Huy-Qui Bui
    • 1
  • Mitchell H. Taibleson
    • 2
  1. 1.Department of MathematicsUniversity of CanterburyChristchurch 1New Zealand
  2. 2.Department of MathematicsWashington UniversitySt. Louis

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