# Triebel-Lizorkin spaces on spaces of homogeneous type

Studia Mathematica (1994)

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

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topHan, 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

top- [CF] S.-Y. A. Chang and R. Fefferman, The Calderón-Zygmund decomposition on product domains, Amer. J. Math. 104 (1982), 445-468. Zbl0513.42019
- [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
- [CW1] R. Coifman et G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, Berlin, 1971.
- [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
- [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
- [FJ] M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170. Zbl0716.46031
- [H1] Y.-S. Han, On the Hardy-type spaces, Chinese Quart. J. Math. 1 (1986), 42-64.
- [H2] Y.-S. Han, The Calderón reproducing formula and the Tb theorem, Rev. Mat. Iberoamericana, to appear.
- [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.
- [M] Y. Meyer, Les nouveaux opérateurs de Calderón-Zygmund, Astérisque 131 (1985), 237-254. Zbl0573.42010
- [MS1] R. A. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), 257-270. Zbl0431.46018
- [MS2] R. A. Macías and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type, ibid., 271-309.
- [TW] M. Taibleson and G. Weiss, The molecular characterization of certain Hardy spaces, Astérisque 77 (1980), 67-149. Zbl0472.46041

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