Triebel-Lizorkin spaces on spaces of homogeneous type

Y.-S. Han

Studia Mathematica (1994)

  • Volume: 108, Issue: 3, page 247-273
  • ISSN: 0039-3223

Abstract

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In [HS] the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type were introduced. In this paper, the Triebel-Lizorkin spaces on spaces of homogeneous type are generalized to the case where p 0 < p ≤ 1 ≤ q < ∞ , and a new atomic decomposition for these spaces is obtained. As a consequence, we give the Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type which were introduced by the maximal function characterization in [MS2].

How to cite

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Han, Y.-S.. "Triebel-Lizorkin spaces on spaces of homogeneous type." Studia Mathematica 108.3 (1994): 247-273. <http://eudml.org/doc/216053>.

@article{Han1994,
abstract = {In [HS] the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type were introduced. In this paper, the Triebel-Lizorkin spaces on spaces of homogeneous type are generalized to the case where $p_0 < p ≤ 1 ≤ q < ∞$, and a new atomic decomposition for these spaces is obtained. As a consequence, we give the Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type which were introduced by the maximal function characterization in [MS2].},
author = {Han, Y.-S.},
journal = {Studia Mathematica},
keywords = {spaces of homogeneous type; $H^p$ and Triebel-Lizorkin spaces; Littlewood-Paley S-function; atomic decomposition; Besov and Triebel-Lizorkin spaces on spaces of homogeneous type; Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type; maximal function characterization},
language = {eng},
number = {3},
pages = {247-273},
title = {Triebel-Lizorkin spaces on spaces of homogeneous type},
url = {http://eudml.org/doc/216053},
volume = {108},
year = {1994},
}

TY - JOUR
AU - Han, Y.-S.
TI - Triebel-Lizorkin spaces on spaces of homogeneous type
JO - Studia Mathematica
PY - 1994
VL - 108
IS - 3
SP - 247
EP - 273
AB - In [HS] the Besov and Triebel-Lizorkin spaces on spaces of homogeneous type were introduced. In this paper, the Triebel-Lizorkin spaces on spaces of homogeneous type are generalized to the case where $p_0 < p ≤ 1 ≤ q < ∞$, and a new atomic decomposition for these spaces is obtained. As a consequence, we give the Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type which were introduced by the maximal function characterization in [MS2].
LA - eng
KW - spaces of homogeneous type; $H^p$ and Triebel-Lizorkin spaces; Littlewood-Paley S-function; atomic decomposition; Besov and Triebel-Lizorkin spaces on spaces of homogeneous type; Littlewood-Paley characterization of Hardy spaces on spaces of homogeneous type; maximal function characterization
UR - http://eudml.org/doc/216053
ER -

References

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  1. [CF] S.-Y. A. Chang and R. Fefferman, The Calderón-Zygmund decomposition on product domains, Amer. J. Math. 104 (1982), 445-468. Zbl0513.42019
  2. [Ch] M. Christ, A T(b) theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math. 60/61 (1990), 601-628. Zbl0758.42009
  3. [CW1] R. Coifman et G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, Berlin, 1971. 
  4. [CW2] R. Coifman et G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. Zbl0358.30023
  5. [DJS] G. David, J.-L. Journé et S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana 1 (1985), 1-56. Zbl0604.42014
  6. [FJ] M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170. Zbl0716.46031
  7. [H1] Y.-S. Han, On the Hardy-type spaces, Chinese Quart. J. Math. 1 (1986), 42-64. 
  8. [H2] Y.-S. Han, The Calderón reproducing formula and the Tb theorem, Rev. Mat. Iberoamericana, to appear. 
  9. [HS] Y.-S. Han and E. T. Sawyer, Littlewood-Paley theory on spaces of homogeneous type and classical function spaces, Mem. Amer. Math. Soc., to appear. 
  10. [M] Y. Meyer, Les nouveaux opérateurs de Calderón-Zygmund, Astérisque 131 (1985), 237-254. Zbl0573.42010
  11. [MS1] R. A. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), 257-270. Zbl0431.46018
  12. [MS2] R. A. Macías and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type, ibid., 271-309. 
  13. [TW] M. Taibleson and G. Weiss, The molecular characterization of certain Hardy spaces, Astérisque 77 (1980), 67-149. Zbl0472.46041

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