Characterization of the Besov-Lipschitz and Triebel-Lizorkin spaces the caseq&lt;1

Bui, Huy-Qui; Paluszyński, Maciej; Taibleson, Mitchell H.

doi:10.1007/bf02656489

Cited by 88 publications

(88 citation statements)

References 4 publications

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“…The other direction is the study of weighted function spaces associated with general Muckenhoupt A ∞ weights. This direction of research for Besov and Triebel-Lizorkin spaces was carried over by Bui, Paluszyńskiet al [7,8,9] and Rychkov [30]. One should also note that a significant portion of the theory of function spaces can also be done on the large class of spaces of homogeneous type introduced by Coifman and Weiss [13]; for example, see [25,26,27].…”

Section: Introduction and Statements Of Main Resultsmentioning

confidence: 99%

Anisotropic Triebel-Lizorkin spaces with doubling measures

Bownik

2007

J Geom Anal

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Section: Introduction and Statements Of Main Resultsmentioning

confidence: 99%

Anisotropic Triebel-Lizorkin spaces with doubling measures

Bownik

2007

J Geom Anal

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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

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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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“…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%