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Triebel-Lizorkin spaces on spaces of homogeneous type

Y.-S. Han — 1994

Studia Mathematica

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 $p_{0} < p \leq 1 \leq q < \infty$ , 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].

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