Some new Triebel-Lizorkin spaces on spaces of homogeneous type and their frame characterizations

Yang, Dachun

doi:10.1007/bf02942219

Cited by 19 publications

(23 citation statements)

References 26 publications

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“…for s, p and q as in Definition 6 (see Lemma 2.1 in [21] for the proof); while the restrictions max(0, −s + d(1/p − 1) + ) < β < θ and 0 < γ < θ guarantee that the definitions of the spaces B s pq (X) and F s pq (X) are independent of the choices of β and γ satisfying these conditions by Theorem 3. Thus, if β and γ are as in Definition 6, then…”

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confidence: 99%

Some new spaces of Besov and Triebel–Lizorkin type on homogeneous spaces

Han

Yang

2003

Studia Math.

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Abstract. New norms for some distributions on spaces of homogeneous type which include some fractals are introduced. Using inhomogeneous discrete Calderón reproducing formulae and the Plancherel-Pólya inequalities on spaces of homogeneous type, the authors prove that these norms give a new characterization for the Besov and TriebelLizorkin spaces with p, q > 1 and can be used to introduce new inhomogeneous Besov and Triebel-Lizorkin spaces with p, q ≤ 1 on spaces of homogeneous type. Moreover, atomic decompositions of these new spaces are also obtained. All the results of this paper are new even for R n . [2] include the Euclidean space, the n-torus in R n , the C ∞ compact Riemannian manifolds, the boundaries of Lipschitz domains and, in particular, the Lipschitz manifolds introduced recently by Triebel in [19] and the d-sets in R n . It has been proved by Triebel in [17] that the d-sets in R n include various kinds of fractals; see also [18]. Introduction. Spaces of homogeneous type introduced by Coifman and Weiss inThe homogeneous Besov and Triebel-Lizorkin spaces on spaces of homogeneous type have been studied in [12] and [7]. In [9], the inhomogeneous Besov and Triebel-Lizorkin spaces on spaces of homogeneous type were introduced by use of the generalized Littlewood-Paley g-functions when p, q ≥ 1. In [10], the inhomogeneous Triebel-Lizorkin spaces were generalized to the cases where 0 < p 0 < p ≤ 1 ≤ q < ∞ via the generalized Littlewood-Paley S-functions. The main purpose of this paper is to generalize the inhomogeneous Besov and Triebel-Lizorkin spaces on spaces of homogeneous type to the case where p, q ≤ 1. To do this, we first introduce

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confidence: 99%

Some new spaces of Besov and Triebel–Lizorkin type on homogeneous spaces

Han

Yang

2003

Studia Math.

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“…( (2.18) when p, q < oo and only in C&b(P, y))' with P and y as in (2.18) when max(p, q) = oo. Moreover, in all cases, WfWbP^x) < The proof of this theorem is similar to the proof of the frame characterizations of the Besov space B pq (X) and the Triebel-Lizorkin space F pq (X) in [48]; see also [23,43]. We omit the details here.…”

Section: -))(Zmy)d^y)mentioning

confidence: 60%

Some new Besov and Triebel-Lizorkin spaces associated with para-accretive functions on spaces of homogeneous type

Deng

Yang

2006

J. Aust. Math. Soc.

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Let (X, p, ti) de be a space of homogeneous type with d > 0 and 6 e (0, 1], ft be a para-accretive function, e € (0,9], \s\ < e, and ao 6 (0, 1) be some constant depending on d, e and .$. The authors introduce the Besov space bB pq (X) with a 0 < p < oo and 0 < q < oo, and the Triebel-Lizorkin space bF pq (X) with a 0 < p < oo and an < ^ < oo by first establishing a Plancherel-Polya-type inequality. Moreover, the authors establish the frame and the Littlewood-Paley function characterizations of these spaces. Furthermore, the authors introduce the new Besov space b~l B s pq (X) and the Triebel-Lizorkin space b~ [ F pq (X). The relations among these spaces and the known Hardy-type spaces are presented. As applications, the authors also establish some real interpolation theorems, embedding theorems, Tb theorems, and the lifting property by introducing some new Riesz operators of these spaces.2000 Mathematics subject classification: primary primary 42B35; secondary 46E35, 42B25, 43A99, 47B06,42B20,47A30,47B38.

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“…Han [10,11] studied Triebel-Lizorkin spaces on spaces of homogeneous type, using discrete Littlewood-Paley-Stein analysis. See also [16,18,22]. We recall the definition of Muckenhoupt weights.…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Atomic Decomposition of Weighted Triebel–lizorkin Spaces on Spaces of Homogeneous Type

2010

J. Aust. Math. Soc.

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Some new Triebel-Lizorkin spaces on spaces of homogeneous type and their frame characterizations

Cited by 19 publications

References 26 publications

Some new spaces of Besov and Triebel–Lizorkin type on homogeneous spaces

Some new spaces of Besov and Triebel–Lizorkin type on homogeneous spaces

Some new Besov and Triebel-Lizorkin spaces associated with para-accretive functions on spaces of homogeneous type

Atomic Decomposition of Weighted Triebel–lizorkin Spaces on Spaces of Homogeneous Type

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