Matrix-weighted Besov spaces

Roudenko, Svetlana

doi:10.1090/s0002-9947-02-03096-9

Cited by 76 publications

(62 citation statements)

References 14 publications

(20 reference statements)

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“…We refer to [30], [45] and [2]. Further we mention [26], see also [19,II.6.4], [11] and [34], which are primarily interested in the homogeneous spaces. In this context they worked with more general weights.…”

Section: Besov Spaces and Sequence Spacesmentioning

confidence: 99%

!Entropy Numbers of Embeddings of Weighted Besov Spaces. Ii

Kühn¹,

Leopold²,

Sickel³

et al. 2006

Proceedings of the Edinburgh Mathematical Society

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Section: Besov Spaces and Sequence Spacesmentioning

confidence: 99%

!Entropy Numbers of Embeddings of Weighted Besov Spaces. Ii

Kühn¹,

Leopold²,

Sickel³

et al. 2006

Proceedings of the Edinburgh Mathematical Society

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“…Weighted Besov and Triebel-Lizorkin spaces with Muckenhoupt weights are well known concepts, cf. [1][2][3][4]12,16,35]. In [17] we dealt with general transformation methods from function to appropriate sequence spaces provided by a wavelet decomposition; we essentially concentrated on the example weight…”

Section: Introductionmentioning

confidence: 99%

Nuclear Embeddings in Weighted Function Spaces

Haroske

Skrzypczak

2020

Integr. Equ. Oper. Theory

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We study nuclear embeddings for weighted spaces of Besov and Triebel–Lizorkin type where the weight belongs to some Muckenhoupt class and is essentially of polynomial type. Here we can extend our previous results concerning the compactness of corresponding embeddings. The concept of nuclearity was introduced by A. Grothendieck in 1955. Recently there is a refreshed interest to study such questions. This led us to the investigation in the weighted setting. We obtain complete characterisations for the nuclearity of the corresponding embedding. Essential tools are a discretisation in terms of wavelet bases, operator ideal techniques, as well as a very useful result of Tong about the nuclearity of diagonal operators acting in $$\ell _p$$ ℓ p spaces. In that way we can further contribute to the characterisation of nuclear embeddings of function spaces on domains.

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“…In this section, we show Plancherel-Pôlya inequalities that give us the independence of the choice of ϕ for the definition of weighted Carleson measure spaces. Before proving those, let us recall a basic estimate of Roudenko [12]. Lemma 3.1.…”

Section: Plancherel-pôlya Inequalitiesmentioning

confidence: 99%