Characterizations of weighted Besov and Triebel-Lizorkin spaces via temperatures

Bui, Huy-Qui

doi:10.1016/0022-1236(84)90017-x

Cited by 56 publications

(63 citation statements)

References 9 publications

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“…Finally, there is also significant interest in the study of weighted function spaces associated with general A ∞ weights. This direction of research was carried over by Bui,Paluszyński,and Taibleson [8,9,11,12] for Besov and Triebel-Lizorkin spaces. The weighted Hardy spaces were studied by Strömberg and Torchinsky [40].…”

Section: Introduction and Statements Of Main Resultsmentioning

confidence: 99%

Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces

Bownik

2005

Trans. Amer. Math. Soc.

158

151

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Abstract. Weighted anisotropic Triebel-Lizorkin spaces are introduced and studied with the use of discrete wavelet transforms. This study extends the isotropic methods of dyadic ϕ-transforms of Jawerth (1985, 1989) to non-isotropic settings associated with general expansive matrix dilations and A ∞ weights.In close analogy with the isotropic theory, we show that weighted anisotropic Triebel-Lizorkin spaces are characterized by the magnitude of the ϕ-transforms in appropriate sequence spaces. We also introduce non-isotropic analogues of the class of almost diagonal operators and we obtain atomic and molecular decompositions of these spaces, thus extending isotropic results of Frazier and Jawerth.

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Section: Introduction and Statements Of Main Resultsmentioning

confidence: 99%

Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces

Bownik

2005

Trans. Amer. Math. Soc.

158

151

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“…The above spaces with weights of type w ∈ A ∞ have been studied systematically by Bui first in [3,4], with subsequent papers [5,6]. It turned out that many of the results from the unweighted situation have weighted counterparts: e.g., we have…”

Section: Definition 22mentioning

confidence: 99%

“…Further details can be found in [3,4,14,30]. Rychkov extended in [31] the above class of weights in order to incorporate locally regular weights, too, creating in that way the class A loc p .…”

Section: 4] and In Particularmentioning

confidence: 99%

Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. General weights

Haroske¹,

Skrzypczak²

2011

Ann. Acad. Sci. Fenn. Math.

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“…This definition has been used by Bui [3,4]. Historical remarks, references, and an exaustive treatment of the "unweighted" case w ≡ 1 can also be found in Triebel [28,29].…”

Section: Preliminariesmentioning

confidence: 99%

“…The well -known A p weights. For this case see, e.g., Kurtz [13], Bui [2,3,4], Strömberg and Torchinsky [26], Bui, Paluszyński, and Taibleson [5,6]. On the contrary to (0.1), a weight w ∈ A p may have a rough local behavior, but its averaged growth at infinity is bounded to at most polynomial by the doubling condition on the measure w dx (see, e. g., Stein [25,Ch.…”

Section: Introductionmentioning

confidence: 99%